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Statistica Sinica 33 (2023), 1233-1248

ASYMPTOTIC OPTIMALITY OF CP-TYPE CRITERIA
IN HIGH-DIMENSIONAL MULTIVARIATE LINEAR
REGRESSION MODELS

Shinpei Imori

Hiroshima University

Abstract: We study the asymptotic optimality of CP-type criteria from the perspective of prediction in high-dimensional multivariate linear regression models, where the dimension of a response matrix is large, but does not exceed the sample size. We derive conditions in order that the generalized CP (GCP) exhibits asymptotic loss efficiency (ALE) and asymptotic mean efficiency (AME) in such high-dimensional data. Moreover, we clarify that one of the conditions is necessary for GCP to exhibit both ALE and AME. As a result, we show that the modified CP can claim both ALE and AME, but the original CP cannot in high-dimensional data. The finite-sample performance of the GCP with several tuning parameters is compared by means of a simulation study.

Key words and phrases: Asymptotic theory, high-dimensional statistical inference, model selection/variable selection.

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