A semiparametric basis for combining estimation problems under quadratic loss
成果类型：
Article
署名作者：
Judge, GG; Mittelhammer, RC
署名单位：
University of California System; University of California Berkeley; Washington State University
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1198/016214504000000430
发表日期：
2004
页码：
479-487
关键词：
摘要：
When there is uncertainty concerning the appropriate statistical model-estimator to use in representing the data sampling process, we consider a basis for optimally combining estimation problems. The objective is to produce natural adaptive estimators that are free of subjective choices and tuning parameters. In the context of two competing multivariate linear statistical models-estimators, we demonstrate a semiparametric Stein-like (SPSL) estimator, (beta) over bar((alpha) over cap), that, under quadratic loss, has superior risk performance relative to the conventional least squares estimator. The relationship of the SPSL estimator to the family of Stein estimators is noted, and asymptotic and analytic finite-sample risk properties of the estimator are developed for some special cases. As an application we consider the problem of combining two polar linear models and demonstrate a corresponding SPSL estimator. An extensive sampling experiment is used to investigate the finite-sample performance of the SPSL estimator over a wide range of data sampling designs and symmetric and skewed distributions. Bootstrapping procedures are used to develop confidence sets and serve as a basis for inference.