Mark G. Low

• Nonparametric function estimation
• Statistical decision theory

1. Adaptive estimation and confidence intervals for convex functions and monotone functions (with Tony Cai).

1. Cai, T. Jin, J. & Low, M. (2007).
   Estimation and confidence sets for sparse normal mixtures.
   The Annals of Statistics to appear.

2. Low, M. & Zhou, H. (2007).
   A complement to Le Cam's Theorem
   The Annals of Statistics to appear.

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

4. Cai, T. & Low, M. (2006).
   Adaptive Confidence Balls.
   The Annals of Statistics 34, 202-228.

5. Cai, T. & Low, M. (2006).
   Adaptation under probabilistic error .
   Journal of Multivariate Analysis 97, 231-245.

6. Cai, T. & Low, M. (2005).
   Nonquadratic estimators of a quadratic functional.
   The Annals of Statistics 33, 184-213.

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

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

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

10. Brown, L.D., Carter, A.V., Low, M.G. & Zhang, C. (2004).
    Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift.
    The Annals of Statistics 32, 2074-2097.

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

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

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

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

15. 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.

16. Kang, Y.-G. and Low, M.G. (2002).
    Estimating monotone functions.
    Statistics and Probability Letters 56, 361-367.

17. Cai, T., Low, M. & Zhao, L. (2001).
    Tradeoffs between global and local risks in nonparametric function estimation.
    Technical Report.

18. Cai, T., Low, M. & Zhao, L. (2000).
    Sharp adaptive estimation by a blockwise method .

• Links to my colleagues and our students

Last updated on November 23, 2004.