A semi-parametric basis for combining estimation problems under quadratic loss
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.
(This abstract was borrowed from another version of this item.)
|Date of creation:||2003|
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- Kim T-H. & White H., 2001.
"James-Stein-Type Estimators in Large Samples With Application to the Least Absolute Deviations Estimator,"
Journal of the American Statistical Association,
American Statistical Association, vol. 96, pages 697-705, June.
- Kim, Tae-Hwan & White, Halbert, 2000. "James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt4zq9k3qh, Department of Economics, UC San Diego.
- Kim, Tae-Hwan & White, Halbert, 2000. "James-Stein Type Estimator in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt3mn102zs, Department of Economics, UC San Diego.
- Kim, Tae-Hwan & White, Halbert, 1999. "James-Stein Type Estimators in Large Samples with Application to the Least Absolute Deviations Estimator," University of California at San Diego, Economics Working Paper Series qt9914w10r, Department of Economics, UC San Diego.
- Ullah, Aman & Ullah, Shobha, 1978. "Double k-Class Estimators of Coefficients in Linear Regression," Econometrica, Econometric Society, vol. 46(3), pages 705-22, May.
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