Multiple shrinkage estimators in multiple linear regression
Titel:
Multiple shrinkage estimators in multiple linear regression
Auteur:
Ki, Yuen-Ching Fanny
Verschenen in:
Communications in statistics
Paginering:
Jaargang 21 (1992) nr. 1 pagina's 111-136
Jaar:
1992
Inhoud:
Consider a standard multiple linear regression model [image omitted] . The usual least squares estimator of β[image omitted] , is dominated by Stein-typed shrinkage estimators; each shrinks [image omitted] to a prior subspace specified by a linear restriction in the form of Cm×pβ = dm×1 where m≤p. However, the reduction in expected sum of prediction squared errors is significant only in a small region in the param-eter space around the prior subspace. The multiple shrinkage estimators, which were first introduced by George (1986), are applied. In multiple linear regression, a multiple shrinkage estimator, which shrinks to more than one prior subspace simultaneously, is shown to dominate [image omitted] . It does not only enlarge the region in the parameter space that gives significant reduction in expected sum of prediction squared errors over that of [image omitted] , but also helps in solving the problem of model selection. A computer simulation is done to show that multiple shrinkage estimators are preferred to estimators given by the stepwise regression procedure in most cases. Lastly, the multiple shrink-age technique is applied to real data analysis examples, which give evidence that multiple shrinkage estimators have better prediction power.
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