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Consistent variable selection criteria in multivariate linear regression even when dimension exceeds sample size

小田 凌也 広島大学

2020.03.23

概要

Multivariate linear regression is an important and very widely used inferential statistical methodology. It is the cornerstone of many theoretical and applied statistics textbooks (see, e.g., Srivastava, 2002, chap 9; Timm, 2002, chap
4) and it has widespread applications in many fields. Let Y = (y(1) , . . . , y(n) )′
be an n × p observation matrix stacking individual p response variables, and
X = (x(1) , . . . , x(n) )′ be an n × k observation matrix stacking individual nonstochastic k explanatory variables, where n is the sample size. Note that X
may include the intercept term that the column vector is 1n ,where 1n is an
n-dimensional vector of ones. Assume that rank(X) = k < n to ensure the
existence of variable selection criteria used in this paper. We consider linear
regression for n samples of a vector of individual p response variables and k ex′
planatory variables on {(y(i)
, x′(i) )′ | i = 1, . . . , n}. Then, the multivariate linear
regression is written as
Y = XΘ + E,
The author is supported financially by Research Fellowships of the Japan Society for the
Promotion of Science for Young Scientists.
2010 Mathematics Subject Classification. Primary 62J05; Secondary 62H12.
Key words and phrases. Hybrid-ultra-high-dimensional asymptotic framework, Multivariate
linear regression, Non-normality, Selection consistency, Variable selection criterion. ...

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Ryoya Oda

Department of Mathematics

Graduate School of Science

Hiroshima University

Higashi-Hiroshima 739-8526, JAPAN

E-mail : ryoya-oda@hiroshima-u.ac.jp

...

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