High-Dimensional Statistical Inference

    Inference for High-Dimensional Covariance Structures

  1. Cai, T. T., Han, X., & Pan, G. (2017).
    Limiting laws for divergent spiked eigenvalues and largest non-spiked eigenvalue of sample covariance matrices.
    Technical report.

  2. Cai, T. T. & Zhang, A. (2017+).
    Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
    The Annals of Statistics, to appear.

  3. Xia, Y., Cai, T. & Cai, T. T. (2017+).
    Multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions.
    Journal of the American Statistical Association, to appear.

  4. Cai, T. T. & Zhang, A. (2016).
    Minimax rate-optimal estimation of high-dimensional covariance matrices with incomplete data.
    Journal of Multivariate Analysis 150, 55-74.

  5. Cai, T. T. & Yuan, M. (2016).
    Minimax and adaptive estimation of covariance operator for random variables observed on a lattice graph.
    Journal of the American Statistical Association 111, 253-265.

  6. Cai, T. T. & Liu, W. (2016).
    Large-scale multiple testing of correlations.
    Journal of the American Statistical Association 111, 229-240.

  7. Cai, T. T., Ren, Z. & Zhou, H. (2016).
    Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (with discussion).
    Electronic Journal of Statistics 10, 1-59.
    (Rejoinder)

  8. Cai, T. T. & Zhang, A. (2016).
    Inference for high-dimensional differential correlation matrices.
    Journal of Multivariate Analysis 143, 107–126.

  9. Cai, T. T., Li, H., Liu, W. & Xie, J. (2016).
    Joint estimation of multiple high-dimensional precision matrices.
    Statistica Sinica 26, 445-464.

  10. Cai, T. T., Liu, W. & Zhou, H. (2016).
    Estimating sparse precision matrix: Optimal rates of convergence and adaptive estimation.
    The Annals of Statistics 44, 455-488.

  11. Xia, Y., Cai, T. & Cai, T. T. (2015).
    Testing differential networks with applications to detecting gene-by-gene interactions.
    Biometrika 102, 247-266.

  12. Cai, T. T., Liang, T. & Zhou, H. (2015).
    Law of log determinant of sample covariance matrix and optimal estimation of differential entropy for high-dimensional Gaussian distributions.
    Journal of Multivariate Analysis 137, 161-172.

  13. Cai, T. T., Ma, Z. & Wu, Y. (2015).
    Optimal estimation and rank detection for sparse spiked covariance matrices.
    Probability Theory and Related Fields 161, 781-815.

  14. Zhao, S.D., Cai, T. T. & Li, H. (2014).
    Direct estimation of differential networks.
    Biometrika 101, 253-268.

  15. Cai, T. T., Ma, Z. & Wu, Y. (2013).
    Sparse PCA: Optimal rates and adaptive estimation.
    The Annals of Statistics 41, 3074-3110.

  16. Cai, T. T. & Ma, Z. (2013).
    Optimal hypothesis testing for high dimensional covariance matrices.
    Bernoulli 19, 2359-2388.

  17. Cai, T. T., Ren, Z. & Zhou, H. (2013).
    Optimal rates of convergence for estimating Toeplitz covariance matrices.
    Probability Theory and Related Fields 156, 101-143.

  18. Cai, T. T., Liu, W. & Xia, Y. (2013).
    Two-sample covariance matrix testing and support recovery in high-dimensional and sparse settings.
    Journal of the American Statistical Association 108, 265-277.

  19. Cai, T. T., Li, H., Liu, W. & Xie, J. (2013).
    Covariate adjusted precision matrix estimation with an application in genetical genomics.
    Biometrika 100, 139-156.

  20. Cai, T. T. & Zhou, H. (2012).
    Optimal rates of convergence for sparse covariance matrix estimation.
    The Annals of Statistics 40, 2389-2420.

  21. Cai, T. T. & Zhou, H. (2012).
    Minimax estimation of large covariance matrices under l1 norm (with discussion).
    Statistica Sinica 22, 1319-1378.

  22. Cai, T. T. & Yuan, M. (2012).
    Adaptive covariance matrix estimation through block thresholding.
    The Annals of Statistics 40, 2014-2042.

  23. Cai, T. T. & Jiang, T. (2012).
    Phase transition in limiting distributions of coherence of high-dimensional random matrices.
    Journal of Multivariate Analysis 107, 24-39.

  24. Cai, T. T. & Liu, W. (2011).
    Adaptive thresholding for sparse covariance matrix estimation.
    Journal of the American Statistical Association 106, 672-684.

  25. Cai, T. T., Liu, W. & Luo, X. (2011).
    A constrained l1 minimization approach to sparse precision matrix estimation.
    Journal of the American Statistical Association 106, 594-607.

  26. Cai, T. T. & Jiang, T. (2011).
    Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
    The Annals of Statistics 39, 1496-1525.

  27. Cai, T. T., Zhang, C.-H. & Zhou, H. (2010).
    Optimal rates of convergence for covariance matrix estimation.
    The Annals of Statistics 38, 2118-2144.

     

    Compressed Sensing & Inference for High-Dimensional Linear Models

  28. Guo, Z., Wang, W., Cai, T. T., & Li, H. (2017+).
    Optimal estimation of genetic relatedness in high-dimensional linear models.
    Journal of the American Statistical Association, to appear.

  29. Cai, T. T. & Guo, Z. (2017+).
    Accuracy assessment for high-dimensional linear regression.
    The Annals of Statistics, to appear.

  30. Guo, Z., Kang, H., Cai, T. T. & Small, D. (2016).
    Confidence intervals for causal effects with invalid instruments using two-stage hard thresholding with voting.
    Technical report.

  31. Kang, H., Cai, T. T. & Small, D. (2015).
    Robust confidence intervals for causal effects with possibly invalid instruments.
    Technical report.

  32. Xia, Y., Cai, T., & Cai, T. T. (2018).
    Two-sample tests for high-dimensional linear regression with an application to gene and environment interactions.
    Statistica Sinica 28, 63-92.

  33. Cai, T. T. & Guo, Z. (2017).
    Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
    The Annals of Statistics 45, 615-646.

  34. Cai, T. T., Liang, T. & Rakhlin, A. (2016).
    Geometric inference for general high-dimensional linear inverse problems.
    The Annals of Statistics 44, 1536–1563.

  35. Kang, H., Zhang, A., Cai, T. T. & Small, D. (2016).
    Instrumental variables estimation with some invalid instruments and its application to Mendelian randomization.
    Journal of the American Statistical Association 111, 132-144.

  36. Zhao, S.D., Cai, T. T., & Li, H. (2014).
    More powerful genetic association testing via a new statistical framework for integrative genomics.
    Biometrics 70, 881-890.

  37. Cai, T. T. & Yuan, M. (2014).
    Discussion: "A Significant Test for Lasso".
    The Annals of Statistics 42, 478-482.

  38. Cai, T. T. & Zhang, A. (2013).
    Compressed sensing and affine rank minimization under restricted isometry.
    IEEE Transactions on Signal Processing 61, 3279-3290.

  39. Cai, T. T. & Zhang, A. (2013).
    Sharp RIP bound for sparse signal and low-rank matrix recovery.
    Applied And Computational Harmonic Analysis 35, 74-93.

  40. Cai, T. T. & Wang, L. (2011).
    Orthogonal matching pursuit for sparse signal recovery with noise.
    IEEE Transactions on Information Theory 57, 4680-4688.

  41. Cai, T. T., Wang, L. & Xu, G. (2010).
    Stable recovery of sparse signals and an oracle inequality.
    IEEE Transactions on Information Theory 56, 3516-3522.

  42. Cai, T. T., Wang, L. & Xu, G. (2010).
    Shifting inequality and recovery of sparse signals.
    IEEE Transactions on Signal Processing 58, 1300-1308.

  43. Cai, T. T., Xu, G. and Zhang, J. (2009).
    On recovery of sparse signals via l1 minimization.
    IEEE Transactions on Information Theory 55, 3388-3397.

  44. Cai, T. T. & Lv, J. (2007).
    Discussion of "The Dantzig Selector: Statistical estimation when p is much larger than n" by E. Candes and T. Tao.
    The Annals of Statistics 35, 2365-2369.

     

    Inference for High-Dimensional Low-Rank Matrices

  45. Cai, T. T. & Zhang, A. (2017+).
    Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
    The Annals of Statistics, to appear.

  46. Cai, T. T., Li, X. & Ma, Z. (2016).
    Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow.
    The Annals of Statistics 44, 2221-2251.

  47. Cai, T. T. & Zhou, W. (2016).
    Matrix completion via max-norm constrained optimization.
    Electronic Journal of Statistics 10, 1493-1525.

  48. Cai, T., Cai, T. T. & Zhang, A. (2016).
    Structured matrix completion with applications to genomic data integration.
    Journal of the American Statistical Association 111, 621-633.

  49. Cai, T. T., Liang, T. & Rakhlin, A. (2016).
    Geometric inference for general high-dimensional linear inverse problems.
    The Annals of Statistics 44, 1536–1563.

  50. Cai, T. T. & Zhang, A. (2015).
    ROP: Matrix recovery via rank-one projections.
    The Annals of Statistics 43, 102-138.

  51. Cai, T. T. & Zhang, A. (2014).
    Sparse representation of a polytope and recovery of sparse signals and low-rank matrices.
    IEEE Transactions on Information Theory 60, 122-132.

  52. Cai, T. T. & Zhou, W. (2013).
    A max-norm constrained minimization approach to 1-bit matrix completion.
    Journal of Machine Learning Research 14, 3619-3647.

  53. Cai, T. T. & Zhang, A. (2013).
    Compressed sensing and affine rank minimization under restricted isometry.
    IEEE Transactions on Signal Processing 61, 3279-3290.

  54. Cai, T. T. & Zhang, A. (2013).
    Sharp RIP bound for sparse signal and low-rank matrix recovery.
    Applied And Computational Harmonic Analysis 35, 74-93.

     

    Detection & Identification of Sparse Signals

  55. Cai, T. T. & Wu, Y. (2018).
    Statistical and computational limits for sparse matrix detection.
    Technical report.

  56. Zhao, S.D., Cai, T. T., & Li, H. (2017+).
    Optimal detection of weak positive latent dependence between two sequences of multiple tests.
    Journal of Multivariate Analysis, to appear.

  57. Zhao, S.D., Cai, T. T., Cappola, T.P., Margulies, K.B., & Li, H. (2017).
    Sparse simultaneous signal detection for identifying genetically controlled disease genes.
    Journal of the American Statistical Association 112, 1032-1046.

  58. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    Computational and statistical boundaries for submatrix localization in a large noisy matrix.
    The Annals of Statistics 45, 1403-1430.

  59. Cai, T. T. & Sun, W. (2017).
    Optimal screening and discovery of sparse signals with applications to multistage high-throughput studies.
    Journal of the Royal Statistical Society, Series B 79, 197–223.

  60. Jeng, J., Cai, T. T. & Li, H. (2015).
    Sparse segment identifications with applications to DNA copy number variation analysis.
    In Advanced Medical Statistics , 2nd Edition, Y. Lu, J. Fang, L., Tian, and H. Jin, eds., World Scientific, New Jersey, 863-887.

  61. Cai, T. T. & Xia, Y. (2014).
    High-Dimensional Sparse MANOVA.
    Journal of Multivariate Analysis 131, 174-196.

  62. Cai, T. T. & Yuan, M. (2014).
    Rate-optimal detection of very short signal segments.
    Technical report.

  63. Cai, T. T. & Wu, Y. (2014).
    Optimal detection for sparse mixtures against a given null distribution.
    IEEE Transactions on Information Theory 60, 2217-2232.

  64. Cai, T. T., Liu, W. & Xia, Y. (2014).
    Two-sample test of high dimensional means under dependence.
    Journal of the Royal Statistical Society, Series B 76, 349-372.

  65. Jeng, J., Cai, T. T. & Li, H. (2013).
    Simultaneous discovery of rare and common segment variants.
    Biometrika 100, 157-172.

  66. Cai, T. T., Jeng, J. & Li, H. (2012).
    Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
    Journal of the Royal Statistical Society, Series B 74, 773-797.

  67. Cai, T. T., Jeng, J. & Jin, J. (2011).
    Optimal detection of heterogeneous and heteroscedastic mixtures.
    Journal of the Royal Statistical Society, Series B 73, 629-662.

  68. Xie, J., Cai, T. T. & Li, H. (2010).
    Sample size and power analysis for sparse signal recovery in genome-wide association studies.
    Biometrika 98, 273-290.

  69. Jeng, J., Cai, T. T. & Li, H. (2010).
    Optimal sparse segment identification with application in copy number variation analysis.
    Journal of the American Statistical Association 105, 1156-1166.

  70. Cai, T. T. Jin, J. & Low, M. (2007).
    Estimation and confidence sets for sparse normal mixtures.
    The Annals of Statistics 35, 2421-2449.

     

    Supervised, Unsupervised, & Semi-Supervised Learning

  71. Zhang, A., Brown, L. D., & Cai, T. T. (2016).
    Semi-supervised inference: General theory and estimation of means.
    Technical report.

  72. Cai, T. T. & Zhang, L. (2016).
    Discussion of "Influential Feature PCA for High Dimensional Clustering".
    The Annals of Statistics 44, 2372-2381.

  73. Cai, T. T. & Liu, W. (2011).
    A direct estimation approach to sparse linear discriminant analysis.
    Journal of the American Statistical Association 106, 1566-1577.

     

    Network Data Analysis

  74. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    Weighted message passing and minimum energy flow for heterogeneous stochastic block models with side information.
    Technical report.

  75. Cai, T. T., Liang, T. & Rakhlin, A. (2016).
    Inference via message passing on partially labelled stochastic block models.
    Technical report.

  76. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    On detection and structural reconstruction of small world random networks.
    IEEE Transactions on Network Science and Engineering 4, 165-176.

  77. Cai, T. T. & Li, X. (2015).
    Robust and computationally feasible community detection in the presence of arbitrary outlier nodes.
    The Annals of Statistics 43, 1027-1059.

     

    Other High-Dimensional Problems

  78. Cai, T. T. & Zhang, A. (2017+).
    Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics.
    The Annals of Statistics, to appear.

  79. Cai, T. T. & Zhang, L. (2017+).
    High-dimensional Gaussian copula regression: Adaptive estimation and statistical inference.
    Statistica Sinica, to appear.

  80. Cai, T. T., Liang, T., & Rakhlin, A. (2017).
    Computational and statistical boundaries for submatrix localization in a large noisy matrix.
    The Annals of Statistics 45, 1403-1430.

  81. Cai, T. T., Li, X. & Ma, Z. (2016).
    Optimal rates of convergence for noisy sparse phase retrieval via thresholded Wirtinger flow.
    The Annals of Statistics 44, 2221-2251.

  82. Cai, T. T., Kim, D., Wang, Y., Yuan, M. & Zhou, H. (2016).
    Optimal large-scale quantum state tomography with Pauli measurements.
    The Annals of Statistics 44, 681-712.

  83. Cai, T. T., Eldar, Y. C. & Li, X. (2016).
    Global testing against sparse alternatives in time-frequency analysis.
    The Annals of Statistics 44, 1438–1466.

  84. Cai, T. T., Liang, T. & Rakhlin, A. (2016).
    Geometric inference for general high-dimensional linear inverse problems.
    The Annals of Statistics 44, 1536–1563.

  85. Cai, T. T. & Xia, Y. (2014).
    High-Dimensional Sparse MANOVA.
    Journal of Multivariate Analysis 131, 174-196.

  86. Cai, T. T., Liu, W. & Xia, Y. (2014).
    Two-sample test of high dimensional means under dependence.
    Journal of the Royal Statistical Society, Series B 76, 349-372.

  87. Cai, T. T., Fan, J. & Jiang, T. (2013).
    Distributions of angles in random packing on spheres.
    Journal of Machine Learning Research 14, 1837-1864.

  88. Cai, T. T. & Jiang, T. (2012).
    Phase transition in limiting distributions of coherence of high-dimensional random matrices.
    Journal of Multivariate Analysis 107, 24-39.

  89. Cai, T. T. & Jiang, T. (2011).
    Limiting laws of coherence of random matrices with applications to testing covariance structure and construction of compressed sensing matrices.
    The Annals of Statistics 39, 1496-1525.

     

    Large-Scale Multiple Testing

  90. Cai, T. T., Sun, W., & Wang, W. (2017).
    CARS: Covariate assisted ranking and screening for large-scale two-sample inference.
    Technical report.

  91. Xiang, D., Zhao, S. D., & Cai, T. T. (2017).
    Signal classification for the integrative analysis of multiple sequences of multiple tests.
    Technical report.

  92. Xia, Y., Cai, T. T. & Li, H. (2017+).
    Joint testing and false discovery rate control for high-dimensional multivariate regression.
    Biometrika, to appear.

  93. Cai, T., Cai, T. T., Liao, K., & Liu, W. (2017+).
    Large-scale simultaneous testing of cross-covariance matrix with applications to PheWAS.
    Statistica Sinica, to appear.

  94. Basu, P., Cai, T. T., Das, K., & Sun, W. (2017+).
    Weighted false discovery rate control in large-scale multiple testing.
    Journal of the American Statistical Association, to appear.

  95. Xia, Y., Cai, T. & Cai, T. T. (2017+).
    Multiple testing of submatrices of a precision matrix with applications to identification of between pathway interactions.
    Journal of the American Statistical Association, to appear.

  96. Xia, Y., Cai, T., & Cai, T. T. (2018).
    Two-sample tests for high-dimensional linear regression with an application to gene and environment interactions.
    Statistica Sinica 28, 63-92.

  97. Cai, T. T. & Sun, W. (2017).
    Large-scale global and simultaneous inference: Estimation and testing in very high dimensions.
    Annual Review of Economics 9, 411-439.

  98. Cai, T. T. (2017).
    Global testing and large-scale multiple testing for high-dimensional covariance structures.
    Annual Review of Statistics and Its Applications 4, 423–446.

  99. Cai, T. T. & Liu, W. (2016).
    Large-scale multiple testing of correlations.
    Journal of the American Statistical Association111, 229-240.

  100. Xia, Y., Cai, T. & Cai, T. T. (2015).
    Testing differential networks with applications to detecting gene-by-gene interactions.
    Biometrika 102, 247-266.

  101. Sun, W., Reich, B. J., Cai, T. T., Guindani, M. & Schwartzman, A. (2015).
    False discovery control in large-scale spatial multiple testing.
    Journal of the Royal Statistical Society, Series B 77, 59-83.

  102. Xie, J., Cai, T. T., Maris, J. & Li, H. (2011).
    Optimal false discovery rate control for dependent data.
    Statistics and Its Interface 4, 417-430.

  103. Cai, T. T. & Jin, J. (2010).
    Optimal rates of convergence for estimating the null and proportion of non-null effects in large-scale multiple testing.
    The Annals of Statistics 38, 100-145.

  104. Cai, T. T. and Sun, W. (2010).
    A compound decision-theoretic approach to large-scale multiple testing.
    In High-Dimensional Data Analysis , T. T. Cai and X. Shen, eds., World Scientific, New Jersey, 75-116.

  105. Cai, T. T. (2010).
    Comments on "Correlated z-values and the Accuracy of Large-Scale Statistical Estimates" by Bradley Efron.
    Journal of the American Statistical Association 105, 1055-1056.

  106. Cai, T. T. & Sun, W. (2009).
    Simultaneous testing of grouped hypotheses: Finding needles in multiple haystacks.
    Journal of the American Statistical Association 104, 1467 - 1481.

  107. Sun, W. & Cai, T. T. (2009).
    Large-scale multiple testing under dependency.
    Journal of the Royal Statistical Society, Series B 71, 393-424.

  108. Sun, W. & Cai, T. T. (2007).
    Oracle and adaptive compound decision rules for false discovery rate control.
    Journal of the American Statistical Association 102, 901-912.

  109. Jin, J. & Cai, T. T. (2007).
    Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
    Journal of the American Statistical Association 102, 495-506.

  110. Cai, T. T. (2008).
    Discussion of "Microarrays, Empirical Bayes, and the Two-Group Model" by Bradley Efron.
    Statistical Science 23, 29-33.

     

    Functional Data Analysis

  111. Cai, T. T., Zhang, L., & Zhou, H. H. (2017+).
    Adaptive functional linear regression via functional principal component analysis and block thresholding.
    Statistica Sinica, to appear.

  112. Cai, T. T. & Yuan, M. (2012).
    Minimax and adaptive prediction for functional linear regression.
    Journal of the American Statistical Association 107, 1201-1216.

  113. Cai, T. T. & Yuan, M. (2011).
    Optimal estimation of the mean function based on discretely sampled functional data: Phase transition.
    The Annals of Statistics 39, 2330-2355.

  114. Cai, T. T. & Yuan, M. (2010).
    Nonparametric covariance function estimation for functional and longitudinal data.
    Technical Report.

  115. Yuan, M. & Cai, T. T. (2010).
    A reproducing kernel Hilbert space approach to functional linear regression.
    The Annals of Statistics 38, 3412-3444.

  116. Cai, T. T. & Hall, P. (2006).
    Prediction in functional linear regression.
    The Annals of Statistics 34, 2159-2179.

     

    Theory & Methodology for Nonparametric Function Estimation

  117. Cai, T. T., Guntuboyina, A., & Wei, Y. (2017+).
    Adaptive estimation of planar convex sets.
    The Annals of Statistics, to appear.

  118. Cai, T. T. & Low, M. (2015).
    A framework for estimation of convex functions.
    Statistica Sinica 25, 423-456.

  119. Cai, T. T., Low, M. & Ma, Z. (2014).
    Adaptive confidence bands for nonparametric regression functions.
    Journal of the American Statistical Association 109, 1054-1070.

  120. Cai, T. T., Low, M. & Xia, Y. (2013).
    Adaptive confidence intervals for regression functions under shape constraints.
    The Annals of Statistics 41, 722-750.

  121. Cai, T. T. (2012).
    Minimax and adaptive inference in nonparametric function estimation.
    Statistical Science 27, 31-50.

  122. Wang, L., Brown, L.D. & Cai, T. T. (2011).
    A difference based approach to the semiparametric partial linear model.
    Electronic Journal of Statistics 5, 619-641.

  123. Cai, T. T. & Low, M. (2011).
    Testing composite hypotheses, Hermite polynomials, and optimal estimation of a nonsmooth functional.
    The Annals of Statistics 39, 1012-1041.

  124. Cai, T. T. & Zhou, H. (2010).
    Nonparametric regression in natural exponential families.
    In Borrowing Strength: Theory Powering Applications -- A Festschrift for Lawrence D. Brown, IMS Collections Vol. 6, 199-215.

  125. Cai, T. T. & Zhou, H. (2009).
    Asymptotic equivalence and adaptive estimation for robust nonparametric regression.
    The Annals of Statistics 37, 3204-3235.

  126. Cai, T. T. (2008).
    On information pooling, adaptability and superefficiency in nonparametric function estimation.
    Journal of Multivariate Analysis 99, 412-436.

  127. Cai, T. T., Low, M. & Zhao, L. (2007).
    Tradeoffs between global and local risks in nonparametric function estimation.
    Bernoulli 13, 1-19.

  128. Cai, T. T. & Hall, P. (2006).
    Prediction in functional linear regression.
    The Annals of Statistics 34, 2159-2179.

  129. Cai, T. T. & Low, M. (2005).
    Nonparametric function estimation over shrinking neighborhoods: Superefficiency and adaptation.
    The Annals of Statistics 33, 184-213.

  130. Cai, T. T. (2003).
    Rates of convergence and adaptation over Besov spaces under pointwise risk.
    Statistica Sinica 13, 881-902.

  131. Brown, L.D., Cai, T. T., Low, M.G. & Zhang, C. (2002).
    Asymptotic equivalence theory for nonparametric regression with random design.
    The Annals of Statistics 30, 688-707.

     

    Wavelet Thresholding

  132. Cai, T. T. & Zhou, H. (2010).
    Nonparametric regression in natural exponential families.
    In Borrowing Strength: Theory Powering Applications -- A Festschrift for Lawrence D. Brown, IMS Collections Vol. 6, 199-215.

  133. Brown, L. D., Cai, T. T. & Zhou, H. (2010).
    Nonparametric regression in exponential families.
    The Annals of Statistics 38, 2005-2046.

  134. Brown, L. D., Cai, T. T., Zhang, R., Zhao, L. & Zhou, H. (2010).
    The root-unroot algorithm for density estimation as implemented via wavelet block thresholding.
    Probability Theory and Related Fields 146, 401-433.

  135. Cai, T. T. & Zhou, H. (2009).
    Asymptotic equivalence and adaptive estimation for robust nonparametric regression.
    The Annals of Statistics 37, 3204-3235.

  136. Cai, T. T. & Zhou, H. (2009).
    A data-driven block thresholding approach to wavelet estimation.
    The Annals of Statistics 37, 569-595.

  137. Cai, T. T., Low, M. & Zhao, L. (2009).
    Sharp adaptive estimation by a blockwise method.
    Journal of Nonparametric Statistics 21, 839-850.

  138. Cai, T. T. & Wang, L. (2008).
    Adaptive variance function estimation in heteroscedastic nonparametric regression.
    The Annals of Statistics 36, 2025-2054.

  139. Brown, L. D., Cai, T. T. & Zhou, H. (2008).
    Robust nonparametric estimation via wavelet median regression.
    The Annals of Statistics 36, 2055-2084.

  140. Chicken, E. & Cai, T. T. (2005).
    Block thresholding for density estimation: Local and global adaptivity.
    Journal of Multivariate Analysis 95, 76-106.

  141. Cai, T. T. (2003).
    Rates of convergence and adaptation over Besov spaces under pointwise risk.
    Statistica Sinica 13, 881-902.

  142. Cai, T. T. (2002).
    On adaptive wavelet estimation of a derivative and other related linear inverse problems.
    J. Statistical Planning and Inference 108, 329-349.

  143. Cai, T. T. (2002).
    On block thresholding in wavelet regression: Adaptivity, block size, and threshold level.
    Statistica Sinica 12, 1241-1273.

  144. Cai, T. T. (2001).
    Discussion on "regularization of wavelets approximations" by A. Antoniadis and J. Fan.
    Journal of the American Statistical Association 96, 960-962.

  145. Cai, T. T., Zhang, D. & Ben-Amotz, D. (2001).
    Enhanced chemical classification of Raman images using wavelet transformation.
    Applied Spectroscopy 55, 1124-1130.

  146. Cai, T. T. & Silverman, B.W. (2001).
    Incorporating information on neighboring coefficients into wavelet estimation.
    Sankhya 63, 127-148.

  147. Cai, T. T. (1999).
    Adaptive wavelet estimation: a block thresholding and oracle inequality approach.
    The Annals of Statistics 27, 898-924.

  148. Cai, T. T. & Brown, L.D. (1999).
    Wavelet estimation for samples with random uniform design.
    Statistics and Probability Letters 42, 313-321.

  149. Cai, T. T. & Brown, L.D. (1998).
    Wavelet shrinkage for nonequispaced samples.
    The Annals of Statistics 26, 1783-1799.

     

    Variance Function Estimation

  150. Cai, T. T., Munk, A. & Schmidt-Hieber, J. (2010).
    Sharp minimax estimation of the variance of Brownian motion corrupted with Gaussian noise.
    Statistica Sinica 20, 1011-1024.

  151. Cai, T. T., Levine, M. & Wang, L. (2009).
    Variance function estimation in multivariate nonparametric regression.
    Journal of Multivariate Analysis 100, 126-136.

  152. Cai, T. T. & Wang, L. (2008).
    Adaptive variance function estimation in heteroscedastic nonparametric regression.
    The Annals of Statistics 36, 2025-2054.

  153. Wang, L., Brown, L. D., Cai, T. T. & Levine, M. (2008).
    Effect of mean on variance function estimation in nonparametric regression.
    The Annals of Statistics 36, 646-664.

     

    Linear/Quadratic Functional Estimation & Uncertainty Quantification

  154. Cai, T. T. & Guo, Z. (2017+).
    Accuracy assessment for high-dimensional linear regression.
    The Annals of Statistics, to appear.

  155. Cai, T. T. & Guo, Z. (2017).
    Confidence intervals for high-dimensional linear regression: Minimax rates and adaptivity.
    The Annals of Statistics 45, 615-646.

  156. Cai, T. T. & Tan, X. L. (2017).
    Optimal estimation of a quadratic functional under the Gaussian two-sequence model.
    Statistica Sinica 27, 879-906.

  157. Cai, T. T., Low, M. & Ma, Z. (2014).
    Adaptive confidence bands for nonparametric regression functions.
    Journal of the American Statistical Association 109, 1054-1070.

  158. Cai, T. T., Low, M. & Xia, Y. (2013).
    Adaptive confidence intervals for regression functions under shape constraints.
    The Annals of Statistics 41, 722-750.

  159. Cai, T. T. (2012).
    Minimax and adaptive inference in nonparametric function estimation.
    Statistical Science 27, 31-50.

  160. Cai, T. T. & Low, M. (2006).
    Optimal adaptive estimation of a quadratic functional.
    The Annals of Statistics 34, 2298-2325.

  161. Cai, T. T. & Low, M. (2006).
    Adaptive confidence balls.
    The Annals of Statistics 34, 202-228.

  162. Cai, T. T. & Low, M. (2006).
    Adaptation under probabilistic error for estimating linear functionals.
    Journal of Multivariate Analysis 97, 231-245.

  163. Cai, T. T. & Low, M. (2005).
    Non-quadratic estimators of a quadratic functional.
    The Annals of Statistics 33, 2930-2956.

  164. Cai, T. T. & Low, M. (2005).
    On adaptive estimation of linear functionals.
    The Annals of Statistics 33, 2311-2343.

  165. Cai, T. T. & Low, M. (2005).
    Adaptive estimation of linear functionals under different performance measures.
    Bernoulli 11, 341-358.

  166. Cai, T. T. & Low, M. (2004).
    An adaptation theory for nonparametric confidence intervals.
    The Annals of Statistics 32, 1805-1840.

  167. Cai, T. T. & Low, M. (2004).
    Minimax estimation of linear functionals over nonconvex parameter spaces.
    The Annals of Statistics 32, 552 - 576.

  168. Cai, T. T. & Low, M. (2003).
    A note on nonparametric estimation of linear functionals.
    The Annals of Statistics 31, 1140-1153.

  169. Cai, T. T. & Low, M. (2002).
    On modulus of continuity and adaptability in nonparametric functional estimation.
    Technical Report.

     

    Inference for Discrete Distributions

  170. Cai, T. T. & Wang, H. (2009).
    Tolerance intervals for discrete distributions in exponential families.
    Statistica Sinica 19, 905-923.

  171. Cai, T. T. (2005).
    One-sided confidence intervals in discrete distributions.
    J. Statistical Planning and Inference 131, 63-88.

  172. Brown, L.D., Cai, T. T. & DasGupta, A. (2005).
    Discussion of "fuzzy and randomized confidence intervals and p-values" by C. J. Geyer and G. D. Meeden.
    Statistical Science 20, 375-379.

  173. Brown, L.D., Cai, T. T. & DasGupta, A. (2003).
    Interval estimation in exponential families.
    Statistica Sinica 13 , 19-49.

  174. Brown, L.D., Cai, T. T. & DasGupta, A. (2002).
    Confidence intervals for a binomial proportion and asymptotic expansions.
    The Annals of Statistics 30, 160-201.

  175. Brown, L.D., Cai, T. T. & DasGupta, A. (2001).
    Interval estimation for a binomial proportion (with discussion).
    Statistical Science 16, 101-133.

     

    Applications

  176. Liao, K. P., Sparks, J. A., Hejblum, B., Kuo, I-H., Cui, J., Lahey, L., Cagan, A., Gainer, V., Liu, W., Cai, T. T., Sokolove, J., & Cai, T. (2017).
    Phenome-wide association study of autoantibodies to citrullinated and non-citrullinated epitopes in rheumatoid arthritis.
    Arthritis & Rheumatology 69, 742-749.

  177. Jeng, J., Cai, T. T. & Li, H. (2013).
    Simultaneous discovery of rare and common segment variants.
    Biometrika 100, 157-172.

  178. Cai, T. T., Li, H., Liu, W. & Xie, J. (2013).
    Covariate adjusted precision matrix estimation with an application in genetical genomics.
    Biometrika 100, 139-156.

  179. Cai, T. T., Jeng, J. & Li, H. (2012).
    Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
    Journal of the Royal Statistical Society, Series B 74, 773-797.

  180. Xie, J., Cai, T. T. & Li, H. (2010).
    Sample size and power analysis for sparse signal recovery in genome-wide association studies.
    Biometrika 98, 273-290.

  181. Jeng, J., Cai, T. T. & Li, H. (2010).
    Optimal sparse segment identification with application in copy number variation analysis.
    Journal of the American Statistical Association 105, 1156-1166.

  182. Jin, J. & Cai, T. T. (2007).
    Estimating the null and the proportion of non-null effects in large-scale multiple comparisons.
    Journal of the American Statistical Association 102, 495-506.

  183. Sun, W. & Cai, T. T. (2007).
    Oracle and adaptive compound decision rules for false discovery rate control.
    Journal of the American Statistical Association 102, 901-912.

  184. Cai, T. T., Zhang, D. & Ben-Amotz, D. (2001).
    Enhanced chemical classification of Raman images using wavelet transformation.
    Applied Spectroscopy 55, 1124-1130.

  185. Shyu, C-R., Cai, T. T. & Broderick, L.S. (1999).
    On archiving and retrieval of sequential images from tomographic databases in PACS.
    Proc. SPIE - the International Society for Optical Engineering 3656, 33-40.

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