On Bickel and Ritov's conjecture about adaptive estimation of the integral of the square of density derivative

Annals of Statistics

Volumn 24, Issue 2, 1996, Pages 682-686

  Efromovich, Sam ^a   Low, Mark ^b  

^a UNIVERSITY OF NEW MEXICO   (United States)

^b UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Adaptation; Functional estimation; Probability density

Indexed keywords

EID: 0030488558     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1032894459     Document Type: Article

References (9)

1. BICKEL, P. J. and RITOV, Y. (1988). Estimating integrated squared density derivatives: sharp best order of convergence estimates. Sankhyā Ser. A 50 381-393.
2. BROWN, L. D. and LOW, M. G. (1993). A constrained risk inequality with applications to nonparametric functional estimation. Ann. Statist. To appear.
3. DEVROYE, L. and GYÖRFI, L. (1985). Nonparametric Density Estimation. Wiley, New York.
4. DONOHO, D. and NUSSBAUM, M. (1990). Minimax quadratic estimation of a quadratic functional. J. Complexity 6 290-323.
5. EFROMOVICH, S. (1985). Nonparametric estimation of a density with unknown smoothness. Theory Probab. Appl. 30 557-568.
6. EFROMOVICH, S. and LOW, M. (1996). On optimal adaptive estimation of a quadratic functional. Ann. Statist. 24 (3).
7. FAN, J. (1991). On the estimation of quadratic functionals. Ann. Statist. 19 1273-1294.
8. p. Theory Probab. Appl. 31 384-389.
9. SERFLING, R. J. (1980). Approximation Theorems of Mathematical Statistics. Wiley, New York.