Adaptive model selection
Xiaotong Shen
The Ohio State University
Model selection becomes increasingly important for analyses involving
a large number of candidate models. In the literature,
most model selection procedures use a fixed penalty penalizing
an increase in the size of a model, including Akaike Information
Criterion (AIC), Mallows's $C_p$, Risk Inflation Criterion (RIC)
and Bayesian Information Criterion (BIC). These non-adaptive selection
procedures perform well only in one type of situations but not across
a variety of situations. In this talk, we will present an
adaptive model selection procedure, based on a data-driven complexity
penalty defined by the concept of generalized degrees of freedom. The proposed
procedure approximates the best performance of a class of model selection
procedures, across a variety of different situations. This class includes
many well-known procedures such as AIC, $C_p$, RIC and BIC. The proposed
procedure is applied to variable selection in least squares regression and
wavelet thresholding in nonparametric regression. Simulation results and
asymptotic analysis support the effectiveness of the proposed procedure.
Based on the joint work with Jimmy Ye.
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