Title :
An asymptotic property of model selection criteria
Author_Institution :
Dept. of Stat., Yale Univ., New Haven, CT, USA
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;
Conference_Titel :
Information Theory and Statistics, 1994. Proceedings., 1994 IEEE-IMS Workshop on
Conference_Location :
Alexandria, VA
Print_ISBN :
0-7803-2761-6
DOI :
10.1109/WITS.1994.513930
