Simultaneous selection and estimation for the some zeros family of normal models

A variable selection proposal for multiple linear regression analysis

“…Venter and Steel [8] use these considerations in an investigation of the multivariate canonical selection problem with B = I and σ 2 = 1. They start by showing that the selection procedure based on the well-known C p −statistic [11] leads to a component-wise pre-test type estimator, viz.…”

“…Within the context of the canonical selection problem described in Section 1, Venter and Steel [8] consider the case where B = I and the value of σ 2 is known, in which case it may be assumed without loss of generality that σ 2 = 1. Their objective is to find an estimatorˆ of θ which is robustly adaptive to sparse configurations, i.e.…”

“…For example, by increasing c, the MSE at θ i = 0 of the resulting estimator is decreased but at the cost of increasing sup θ i MSEˆ i (θ i ). Venter and Steel [8] point out that within the class of symmetric component-wise estimators the LT estimator, with ith component defined byˆ…”

“…Regarding the remainder of the paper, in Section 2, we describe a selection procedure which was introduced by Venter and Steel [8]. This procedure, based on an approximate solution to an optimality problem posed by Bickel [9], is applicable in regression problems only when the observed predictor variables are orthogonal.…”

Pre-Test type estimators for selection of simple normal models

“…Suppose also that 0 belongs to an unknown member of the some zeros family of models (Venter and Steel (1993a), henceforth abbreviated VS (1993a)), i.e. for some unknown r C (1, 2, .…”