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A class of shrinkage estimators in linear regression
Author(s) -
Blaker Helge
Publication year - 1999
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 - 10.2307/3315502
Subject(s) - multicollinearity , estimator , linear subspace , shrinkage , linear regression , mathematics , shrinkage estimator , statistics , regression , principal component analysis , principal component regression , class (philosophy) , regression analysis , sample (material) , econometrics , computer science , artificial intelligence , efficient estimator , minimum variance unbiased estimator , chemistry , geometry , chromatography
We consider the problem of using shrinkage estimators that shrink towards subspaces in linear regression, in particular subspaces spanned by principal components. This is especially important when multicollinearity is present and the number of predictors is not small compared to the sample size. New theoretical results about Stein estimation are used to get estimators with lower theoretical risk than standard Stein estimators used by Oman (1991). Application of the techniques to real data is largely successful.