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- W2000436178 abstract "The AIC, the multivariate Cp 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 Ω=O(np) when p/n→c∈[0,1), where Ω is a noncentrality matrix. In this paper we show that several criteria including HAIC and Cp have also a consistency property under Ω=O(n) as well as Ω=O(np) when p/n→c∈[0,1). Our results are checked numerically by conducting a Monte Carlo simulation." @default.
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- W2000436178 date "2014-01-01" @default.
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- W2000436178 title "Consistency of high-dimensional AIC-type and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si80.gif display=inline overflow=scroll><mml:msub><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:math>-type criteria in multivariate linear regression" @default.
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- W2000436178 doi "https://doi.org/10.1016/j.jmva.2013.09.006" @default.
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