Open Access
March, 1992 Smoothing in Adaptive Estimation
Julian J. Faraway
Ann. Statist. 20(1): 414-427 (March, 1992). DOI: 10.1214/aos/1176348530


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.


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Julian J. Faraway. "Smoothing in Adaptive Estimation." Ann. Statist. 20 (1) 414 - 427, March, 1992.


Published: March, 1992
First available in Project Euclid: 12 April 2007

zbMATH: 0745.62029
MathSciNet: MR1150352
Digital Object Identifier: 10.1214/aos/1176348530

Primary: 62F35
Secondary: 62E25 , 62F11 , 62G20

Keywords: $B$-splines , Adaptation , efficient estimation

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
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