Smoothing in Adaptive Estimation

The Annals of Statistics · 1992 · Volume 20 · Issue 1

Abstract

An adaptive maximum likelihood estimator based on the estimation of the log-density by $B$-splines is introduced. A data-driven method of selecting the smoothing parameter involved in the consequent density estimation is demonstrated. A Monte Carlo study is conducted to evaluate the small sample performance of the estimator in a location and a regression problem. The adaptive estimator is seen to compare favorably to some standard estimates. We show that the estimator is asymptotically efficient.

Keywords

$B$-splines; 62E25; 62F11; 62F35; 62G20; Adaptation; efficient estimation;

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