Papers & Technical Reports by Topics
(Papers in Chronicle Order)

T. Tony Cai

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• High-Dimensional Statistical Inference

• Compressed Sensing

• Large-Scale Multiple Testing

• Functional Data Analysis

• Theory of Nonparametric Function Estimation

• Wavelet Thresholding

• Variance Function Estimation

• Linear Functionals & Nonparametric Confidence Intervals

• Quadratic Functionals & Confidence Balls

• Inference for Discrete Distributions

• Applications to Genomics, Chemical Identification, & Medical Imaging

(Some papers are cross-listed under more than one category.)

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High-Dimensional Statistical Inference
1. Cai, T. & Yuan, M. (2012).
   Adaptive covariance matrix estimation through block thresholding.
   The Annals of Statistics, to appear.

2. Cai, T. & Ma, Z. (2012).
   Optimal hypothesis testing for high dimensional covariance matrices.
   Bernoulli , to appear.

3. Cai, T. & Zhou, H. (2012).
   Optimal rates of convergence for sparse covariance matrix estimation.
   The Annals of Statistics, to appear.

4. Cai, T., Ren, Z. & Zhou, H. (2012).
   Optimal rates of convergence for estimating Toeplitz covariance matrices.
   Probability Theory and Related Fields, to appear.

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

6. Cai, T. & Zhang, A. (2011).
   Sharp RIP bound for sparse signal and low-rank matrix recovery.
   Technical report.

7. Cai, T., Li, H., Liu, W. & Xie, J. (2011).
   Covariate adjusted precision matrix estimation with an application in genetical genomics.
   Technical report.

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

9. Cai, T. & Zhou, H. (2011).
   Minimax estimation of large covariance matrices under l₁ norm (with discussion).
   Statistica Sinica, to appear.

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

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

12. Cai, 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.

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

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

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

16. Cai, T., Jeng, J. & Li, H. (2010).
    Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
    Journal of the Royal Statistical Society, Series B, to appear.

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

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

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

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

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

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

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

24. Cai, 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.

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    Compressed Sensing

25. Cai, T. & Zhang, A. (2011).
    Sharp RIP bound for sparse signal and low-rank matrix recovery.
    Technical report.

26. Cai, T. & Jiang, T. (2011).
    Phase transition in limiting distributions of coherence of high-dimensional random matrices.
    J. Multivariate Analysis, to appear.

27. Cai, 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.

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

29. Cai, T., Wang, L. & Xu, G. (2010).
    New bounds for restricted isometry constants
    IEEE Transactions on Information Theory 56, 4388-4394.

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

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

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

33. Cai, 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.

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    Large-Scale Multiple Testing

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

35. Cai, 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.

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

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

38. Sun, W. and Cai, T. (2008).
    Large-scale multiple testing under dependency.
    Journal of the Royal Statistical Society, Series B 71, 393-424.

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

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

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

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    Functional Data Analysis

42. Cai, T. & Yuan, M. (2011).
    Minimax and adaptive prediction for functional linear regression.
    Technical Report.

43. Cai, 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.

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

45. Yuan, M. & Cai, T. (2008).
    A reproducing kernel Hilbert space approach to functional linear regression.
    The Annals of Statistics 38, 3412-3444.

46. Cai, T. & Zhou, H. (2008).
    Adaptive functional linear regression.
    Technical report.

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

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    Theory of Nonparametric Function Estimation

48. Cai, T. & Low, M. (2012).
    A framework for estimation of convex functions.
    Technical report.

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

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

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

52. Cai, 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.

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

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

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

56. Cai, T. (2006).
    On information pooling, adaptability and superefficiency in nonparametric function estimation.
    J. Multivariate Analysis 99, 412-436.

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

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

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

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    Wavelet Thresholding: Methodology & Theory

60. Cai, 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.

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

62. Brown, L. D., Cai, 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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    Variance Function Estimation

78. Cai, 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.

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

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

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

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    Linear Functionals & Nonparametric Confidence Intervals

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

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

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

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

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

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

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

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    Quadratic Functionals & Confidence Balls

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

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

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

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    Inference for Discrete Distributions

92. Cai, T. & Wang, H. (2009).
    Probability matching tolerance intervals for distributions in exponential families.
    Statistica Sinica 19, 905-923.

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

94. Brown, L.D., Cai, 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.

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

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

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

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    Applications

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

99. Cai, T., Jeng, J. & Li, H. (2010).
    Robust detection and identification of sparse segments in ultra-high dimensional data analysis.
    Journal of the Royal Statistical Society, Series B, to appear.

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

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

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

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

104. Shyu, C-R., Cai, 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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