A Semi-Parametric Basis for Combining Estimation Problems Under Quadratic Loss

George Judge () and Ron Mittelhammer ()

Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series from Department of Agricultural & Resource Economics, UC Berkeley

Abstract: When there is uncertainty concerning the appropriate statistical model to use in representing the data sampling process and corresponding estimators, we consider a basis for optimally combining estimation problems. In the context of the multivariate linear statistical model, we consider a semi-parametric Stein-like (SPSL) estimator, B( ), that shrinks to a random data-dependent vector and, under quadratic loss, has superior performance relative to the conventional least squares estimator. The relationship of the SPSL estimator to the family of Stein estimators is noted and risk dominance extensions between correlated estimators are demonstrated. As an application we consider the problem of a possibly ill-conditioned design matrix and devise a corresponding SPSL estimator. Asymptotic and analytic finite sample risk properties of the estimator are demonstrated. An extensive sampling experiment is used to investigate finite sample performance over a wide range of data sampling processes to illustrate the robustness of the estimator for an array of symmetric and skewed distributions. Bootstrapping procedures are used to develop confidence sets and a basis for inference.

Keywords: Stein-like shrinkage; quadratic loss; ill-conditioned design; semiparametric estimation and inference; data dependent shrinkage vector; asymptotic and finite sample risk (search for similar items in EconPapers)
Date: 2003-01-01
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Citations: View citations in EconPapers (3)

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Related works:
Journal Article: A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss (2004)
Working Paper: A Semi-Parametric Basis for Combining Estimation Problems Under Quadratic Loss (2003)
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Persistent link: https://EconPapers.repec.org/RePEc:cdl:agrebk:qt8z25j0w3

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