On Sequential Data-Driven Density Estimation

Abstract

The theory and methods of minimax and sequential inferences, pioneered by Abraham Wald in 1940's, shaped the way statisticians see the statistics today. This article employs the Wald approaches together with the modern oracle analysis to develop the theory and methods of a sharp minimax adaptive sequential density estimation. In particular, it proves a long-standing conjecture about a sufficient condition for a sharp adaptive sequential estimation with an assigned mean integrated squared error. It also suggests, and then studies via intensive Monte-Carlo simulations, a data-driven sequential density estimator that can be recommended for practical applications.

Key Words:

• Nonparametric
• Minimax
• Oracle
• Small sample

Mathematics Subject Classification:

• 62G05, 62G07
• Secondary 62N01, 62F12

Acknowledgment

The author of this article is supported in part by NSF Grant 0243606.

Notes

Recommened by Nitis Mukhopadhyay