An asymptotic property of model selection criteria

Author

Yang, Yuhong

Author_Institution

Dept. of Stat., Yale Univ., New Haven, CT, USA

fYear

1994

fDate

27-29 Oct 1994

Firstpage

103

Abstract

Probability models are estimated by use of penalized likelihood criteria related to the Akaike (1972) information criteria (AIC) and the minimum description length (MDL). The asymptotic risk of the density estimator is determined, under conditions on the penalty term, and is shown to be minimax optimal. As an application, we show that the optimal rate of convergence is achieved for the density in certain smooth nonparametric families without knowing the smooth parameters in advance

Keywords

convergence of numerical methods; estimation theory; information theory; minimax techniques; nonparametric statistics; probability; smoothing methods; AIC; MDL; asymptotic property; asymptotic risk; density estimator; minimax optimal criterion; model selection criteria; optimal convergence rate; penalized likelihood criteria; probability models; smooth nonparametric families; smooth parameters; Approximation error; Convergence; Density functional theory; Density measurement; Estimation error; Minimax techniques; Parameter estimation; Probability; Spline; Statistics;

fLanguage

English

Publisher

ieee

Conference_Titel

Information Theory and Statistics, 1994. Proceedings., 1994 IEEE-IMS Workshop on

Conference_Location

Alexandria, VA

Print_ISBN

0-7803-2761-6

Type

conf

DOI

10.1109/WITS.1994.513930

Filename

513930

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=2346243