On the asymptotic distributional risk properties of pre-test and shrinkage \(L_ 1\)-estimators
type: Item
instance of: scholarly article
title: On the asymptotic distributional risk properties of pre-test and shrinkage \(L_ 1\)-estimators
zbMATH Open document ID: 0632.62066
DOI: 10.1016/0167-9473(87)90052-1
author: A. K. Md. Ehsanes Saleh
author: Pranab K. Sen
published in: Computational Statistics and Data Analysis
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 62J07
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 4028662
zbMATH Keywords: James-Stein rule
zbMATH Keywords: local alternatives
zbMATH Keywords: preliminary test estimation
zbMATH Keywords: robustness
zbMATH Keywords: shrinkage estimation
zbMATH Keywords: L1 estimation
zbMATH Keywords: general univariate linear model
zbMATH Keywords: asymptotic distributional risks
zbMATH Keywords: relative asymptotic risk- efficiency results
MaRDI profile type: Publication
full work available at URL: 0167-9473(87)90052-1
OpenAlex ID: W1558519126
cites work: On Biases in Estimation Due to the Use of Preliminary Tests of Significance
cites work: Analysis and Inference for Incompletely Specified Models Involving the Use of Preliminary Test(s) of Significance
cites work: Asymptotic Theory of Least Absolute Error Regression
cites work: Q3185327
cites work: Q4178373
cites work: Tests of Linear Hypotheses and l"1 Estimation
cites work: Q3730814
cites work: On shrinkage m-estimators of location parameters
cites work: Relative performance of stein-rule and preliminary test estimators in linear models least squares theory
cites work: Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution
cites work: A james-stein type detour of U-statistics
cites work: Q3831862
cites work: Nonparametric estimation of location parameter after a preliminary test on regression in the multivariate case
cites work: On some shrinkage estimators of multivariate location
cites work: On preliminary test and shrinkage M-estimation in linear models
description: scientific article; zbMATH DE number 4028662