The Annals of Statistics

On Predictive Least Squares Principles

C. Z. Wei

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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.

Article information

Ann. Statist., Volume 20, Number 1 (1992), 1-42.

First available in Project Euclid: 12 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62J05: Linear regression 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

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


Wei, C. Z. On Predictive Least Squares Principles. Ann. Statist. 20 (1992), no. 1, 1--42. doi:10.1214/aos/1176348511.

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