High-dimensional asymptotic expansions for the distributions of canonical correlations
Journal of Multivariate Analysis
An unbiased Cp criterion for multivariate ridge regression
Journal of Multivariate Analysis
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The AIC, the multivariate C"p and their modifications have been proposed for multivariate linear regression models under a large-sample framework when the sample size n is large, but the dimension p of the response variables is fixed. In this paper, first we propose a high-dimensional AIC (denoted by HAIC) which is an asymptotic unbiased estimator of the risk function defined by the expected log-predictive likelihood or equivalently the Kullback-Leibler information under a high-dimensional framework p/n-c@?[0,1). It is noted that our new criterion provides better approximations to the risk function in a wide range of p and n. Recently Yanagihara et al. (2012) [17] noted that AIC has a consistency property under @W=O(np) when p/n-c@?[0,1), where @W is a noncentrality matrix. In this paper we show that several criteria including HAIC and C"p have also a consistency property under @W=O(n) as well as @W=O(np) when p/n-c@?[0,1). Our results are checked numerically by conducting a Monte Carlo simulation.