Sharp estimation in sup norm with random design

Statistics and Probability Letters

Volumn 77, Issue 8, 2007, Pages 782-794

  Gaïffas, Stéphane ^a  

^a UNIVERSITÉ PARIS DESCARTES   (France)

Author keywords

Inhomogeneous data; Non parametric regression; Random design; Sharp estimation

Indexed keywords

EID: 33947641027     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.spl.2006.11.017     Document Type: Article

References (19)

1. Arestov V.V. Optimal recovery of operators and related problems. Proc. Steklov Inst. Math. 4 (1990) 1-20
2. Bertin K. Asymptotically exact minimax estimation in sup-norm for anisotropic Hölder classes. Bernoulli 10 (2004) 873-888
3. Bertin K. Minimax exact constant in sup-norm for nonparametric regression with random design. J. Statist. Plann. Inference 123 (2004) 225-242
4. Brown L.D., and Low M.G. Asymptotic equivalence of nonparametric regression and white noise. Ann. Statist. 24 (1996) 2384-2398
5. Brown L.D., Cai T., Low M.G., and Zhang C.-H. Asymptotic equivalence theory for nonparametric regression with random design. Ann. Statist. 30 (2002) 688-707
6. Donoho D.L. Asymptotic minimax risk for sup-norm loss: solution via optimal recovery. Probab. Theory Related Fields 99 (1994) 145-170
7. Donoho D.L., and Low M.G. Renormalization exponents and optimal pointwise rates of convergence. Ann. Statist. 20 (1992) 944-970
8. Fuller A.T. Relay control systems optimized for various performance criteria. Automat. Remote Control 1 (1961)
9. Gaïffas S. Convergence rates for pointwise curve estimation with a degenerate design. Math. Methods Statist. 1 (2005) 1-27. http://hal.ccsd.cnrs.fr/ccsd-00003086/en/ Available at 〈http://hal.ccsd.cnrs.fr/ccsd-00003086/en/〉
10. Gaïffas, S., 2005b. Sharp estimation in sup norm with random design. Preprint LPMA no. 1010 available at 〈http://hal.ccsd.cnrs.fr/ccsd-00009135/en/〉.
11. Korostelev V. An asymptotically minimax regression estimator in the uniform norm up to exact content. Theory Probab. Appl. 38 (1993) 737-743
12. Korostelev A., and Nussbaum M. The asymptotic minimax constant for sup-norm loss in nonparametric density estimation. Bernoulli 5 (1999) 1099-1118
13. Ledoux, M., Talagrand, M., 1991. Probability in Banach spaces. Ergebnisse der Mathematik und ihrer Grenzgebiete (3), vol. 23 [Results in Mathematics and Related Areas (3)]. Springer, Berlin. Isoperimetry and processes.
14. Leonov S. On the solution of an optimal recovery problem and its applications in nonparametric regression. Math. Methods Statist. 6 (1997) 476-490
15. Leonov S. Remarks on extremal problems in nonparametric curve estimation. Statist. Probab. Lett. 43 (1999) 169-178
16. Lepski O.V., and Tsybakov A.B. Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point. Probab. Theory Related Fields 117 (2000) 17-48
17. Lepski O.V., Mammen E., and Spokoiny V.G. Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. 25 (1997) 929-947
18. Micchelli C.A., and Rivlin T.J. A survey of optimal recovery. Optimal Estimation Approx. Theory 1-54 (1977)
19. Stone C.J. Optimal global rates of convergence for nonparametric regression. Ann. Statist. 10 (1982) 1040-1053