Model Selection with Data-Oriented Penalty.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK CENTER FOR MULTIVARIATE ANALYSIS
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We consider the model selection or variables selection in the classical regression problem. In the literature, there are two types of criteria for model selection, one based on prediction error FPE and another on information theoretic considerations GIC. Each of these criteria uses a certain penalty function which is the product of the number of variables j in a submodel and a function Cn depending on n and satisfying some conditions to guarantee consistency in model selection. One of the important problems in such a procedure is the actual choice of Cn in a given situation. In this paper we show that a particular choice of Cn based on observed data, which makes it random, preserves the consistency property and shows improved performance over a fixed choice of Cn.
- Statistics and Probability
- Operations Research