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Improved set estimators for the coefficients of a linear model when the error distribution is spherically symmetric with unknown variances
Author(s) -
Chen Jeesen,
Hwang Jiunn T.
Publication year - 1988
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3314735
Subject(s) - estimator , confidence interval , mathematics , confidence distribution , variance (accounting) , confidence region , statistics , delta method , linear model , set (abstract data type) , computer science , programming language , accounting , business
The usual confidence set for p ( p ≥ 3) coefficients of a linear model is known to be dominated by the James‐Stein confidence sets under the assumption of spherical symmetric errors with known variance (Hwang and Chen 1986). For the same confidence‐set problem but for the unknown ‐variance case, naturally one replaces the unknown variance by an estimator. For the normal case, many previous studies have shown numerically that the resultant James‐Stein confidence sets dominate the resultant usual confidence sets, i.e., the F confidence sets. In this paper we provide a further asymptotic justification, and we discover the same advantage of the James‐Stein confidence sets for normal error as well as spherically symmetric error.