Consistency of high-dimensional AIC-type and Cp-type criteria in multivariate linear regression

Yasunori Fujikoshi, Tetsuro Sakurai and Hirokazu Yanagihara

Journal of Multivariate Analysis, 2014, vol. 123, issue C, 184-200

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.

Keywords: AIC; Cp; Consistency property; High-dimensional criteria; Modified criteria; Multivariate linear regression (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (6)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X1300198X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:123:y:2014:i:c:p:184-200

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2013.09.006

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().