On the asymptotic distributional risk properties of pre-test and shrinkage \(L_ 1\)-estimators
In a general univariate linear model, \(L_ 1\)-estimation of a subset of parameters is considered when the complementary subset is suspected to be redundant. Along with the \(L_ 1\)-estimation of all the parameters, both preliminary test and shrinkage \(L_ 1\)-estimators based on the usual \(L_ 1\)-estimators are considered. In the light of their asymptotic distributional risks, the relative asymptotic risk-efficiency results are studied in detail. Though the shrinkage \(L_ 1\)-estimator may dominate the usual \(L_ 1\)-estimator, it does not, in general, dominate the preliminary test \(L_ 1\)- estimator.
relative asymptotic risk- efficiency results
scientific article; zbMATH DE number 4028662
scientific article