Rank Theory: Shrinkage and Selection

• Activity Number: 45
• Type: Contributed
• Date/Time: Sunday, August 4, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): A. K. Md. Ehsanes Saleh*+ and Radim Navratil
• Companies: Carleton University and Charles University

Abstract

We propose robust method for the estimation of parameters in linear models with rank theory.In this case, we define the set D_(n)=[ b:??L(b)?? is minimized] subject to S ?b(j)? =t . where L(b) is the vector of LRS for the test of the hypothesis that b=0.Here norm may be l(1) 0r l(2) along with other possibilities.The nature of constraint tend to put some of the coefficients to be exactly zero producing interpretable robust models.The resulting models carry the properties like subset selection and ridge regression estimators. We study ten shrinkage estimators which include the preliminary test and Stein-type estimators together with the ridge regression estimators to verify our assertion with the analysis of prostate data as in Tibshirani(1994) .We also provide expressions of mean square error to compare the estimators with LASSO.Our study complements the study the LASSO estimators in a favourable way.