タニザキ　ヒサシ   Hisashi Tanizaki   谷崎　久志    所属   追手門学院大学  理工学部 数理・データサイエンス学科    職種   教授
言語種別	英語
発行・発表の年月	2004
形態種別	外国学術誌（その他）
査読	査読あり
標題	Exact Distributions of R2 and Adjusted R2 in a Linear Regression Model with Multivariate t Error Terms
執筆形態	共著・編著（代表編著を除く）
掲載誌名	Journal of the Japan Statistical Society
掲載区分	国内
出版社・発行元	The Japan Statistical Society
巻・号・頁	Vol.34, No.1, pp.101-109(1),pp.101-109
担当区分	最終著者
著者・共著者	Kazuhiro Ohtani,Hisashi Tanizaki
概要	In this paper we consider a linear regression model when error terms obey a multivariate t distribution, and examine the effects of departure from normality of error terms on the exact distributions of the coefficient of determination (say, R^2) and adjusted R^2 (say, R^2 ). We derive the exact formulas for the density function, distribution function and m-th moment, and perform numerical analysis based on the exact formulas. It is shown that the upward bias of R^2 gets serious and the standard error of R^2 gets large as the degrees of freedom of the multivariate t error distribution (say, V_0) get small. The confidence intervals of R^2 and R^2 are examined, and it is shown that when the values of V_0 and the parent coefficient of determination (say, Φ) are small, the upper confidence limits are very large, relative to the value of Φ.
DOI	10.14490/jjss.34.101
ISSN	0389-5602
NAID	110003144475
PermalinkURL	http://id.ndl.go.jp/bib/7042932
researchmap用URL	http://id.nii.ac.jp/1141/00022932/