Open Access
March, 1992 On Predictive Least Squares Principles
C. Z. Wei
Ann. Statist. 20(1): 1-42 (March, 1992). DOI: 10.1214/aos/1176348511


Recently, Rissanen proposed a new model selection criterion PLS that selects the model that minimizes the accumulated squares of prediction errors. Usually, the information-based criteria, such as AIC and BIC, select the model that minimizes a loss function which can be expressed as a sum of two terms. One measures the goodness of fit and the other penalizes the complexity of the selected model. In this paper we provide such an interpretation for PLS. Using this relationship, we give sufficient conditions for PLS to be strongly consistent in stochastic regression models. The asymptotic equivalence between PLS and BIC for ergodic models is then studied. Finally, based on the Fisher information, a new criterion FIC is proposed. This criterion shares most asymptotic properties with PLS while removing some of the difficulties encountered by PLS in a finite-sample situation.


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C. Z. Wei. "On Predictive Least Squares Principles." Ann. Statist. 20 (1) 1 - 42, March, 1992.


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

zbMATH: 0801.62083
MathSciNet: MR1150333
Digital Object Identifier: 10.1214/aos/1176348511

Primary: 62M10
Secondary: 62J05 , 62M20

Keywords: AIC , BIC , FIC , Model selection , predictive least squares , predictive minimum description length , stochastic regression , strong consistency

Rights: Copyright © 1992 Institute of Mathematical Statistics

Vol.20 • No. 1 • March, 1992
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