Appropriate penalties in the final prediction error criterion: a decision theoretic approach

Ping Zhang and Abba M. Krieger

Statistics & Probability Letters, 1993, vol. 18, issue 3, 169-177

Abstract: The final prediction error (FPE) criterion has been used widely in model selection. The criterion for a linear regression model with k parameters can be written as RSS(k) + [lambda]k2, where RSS(k) is the residual sums of squares, 2 is an unbiased estimate of the error variance and [lambda] is a penalty for complexity. This article considers the simplest situation where the choice is between two Gaussian linear regression models with 2 assumed to be known. We define a signal to noise ratio b for a regression model and use b to restrict the parameter space. The loss function is chosen to be the squared prediction error. Values of [lambda] that are minimax and values of [lambda] that are admissible are found as a function of b.

Keywords: Constrained; parameter; space; model; selection; post-selection; risk; signal; to; noise; ratio; minimax; and; admissible; criterion (search for similar items in EconPapers)
Date: 1993
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Citations: View citations in EconPapers (1)

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