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A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss

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  • Judge G.G.
  • Mittelhammer R.C.

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.
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Suggested Citation

  • Judge G.G. & Mittelhammer R.C., 2004. "A Semiparametric Basis for Combining Estimation Problems Under Quadratic Loss," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 479-487, January.
  • Handle: RePEc:bes:jnlasa:v:99:y:2004:p:479-487
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    References listed on IDEAS

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    1. 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.
    2. Ullah, Aman & Ullah, Shobha, 1978. "Double k-Class Estimators of Coefficients in Linear Regression," Econometrica, Econometric Society, vol. 46(3), pages 705-722, May.
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    Cited by:

    1. Miller, Douglas J. & Mittelhammer, Ronald C. & Judge, George G., 2004. "Entropy-Based Estimation And Inference In Binary Response Models Under Endogeneity," 2004 Annual meeting, August 1-4, Denver, CO 20319, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    2. Raheem, S.M. Enayetur & Ahmed, S. Ejaz & Doksum, Kjell A., 2012. "Absolute penalty and shrinkage estimation in partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 874-891.
    3. Mittelhammer, Ron C. & Judge, George G., 2005. "Combining estimators to improve structural model estimation and inference under quadratic loss," Journal of Econometrics, Elsevier, vol. 128(1), pages 1-29, September.
    4. Mittelhammer, Ronald C. & Judge, George G. & Miller, Douglas J. & Cardell, N. Scott, 2005. "Minimum Divergence Moment Based Binary Response Models: Estimation and Inference," CUDARE Working Papers 25020, University of California, Berkeley, Department of Agricultural and Resource Economics.
    5. Grendar, Marian & Judge, George G., 2006. "Large Deviations Theory and Empirical Estimator Choice," CUDARE Working Papers 25084, University of California, Berkeley, Department of Agricultural and Resource Economics.
    6. repec:spr:metrik:v:81:y:2018:i:5:d:10.1007_s00184-018-0656-1 is not listed on IDEAS
    7. Judge, George G. & Mittelhammer, Ronald C., 2004. "Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss," CUDARE Working Papers 25095, University of California, Berkeley, Department of Agricultural and Resource Economics.
    8. Judge, George G. & Mittelhammer, Ron C, 2004. "Estimating the Link Function in Multinomial Response Models under Endogeneity and Quadratic Loss," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt4422n50w, Department of Agricultural & Resource Economics, UC Berkeley.
    9. Mittelhammer, Ron C & Judge, George G. & Miller, Douglas J & Cardell, N. Scott, 2005. "Minimum Divergence Moment Based Binary Response Models: Estimation and Inference," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt1546s6rn, Department of Agricultural & Resource Economics, UC Berkeley.
    10. Joshua D. Angrist & Peter D. Hull & Parag A. Pathak & Christopher R. Walters, 2017. "Leveraging Lotteries for School Value-Added: Testing and Estimation," The Quarterly Journal of Economics, Oxford University Press, vol. 132(2), pages 871-919.
    11. Judge, George G. & Mittelhammer, Ron C., 2007. "Estimation and inference in the case of competing sets of estimating equations," Journal of Econometrics, Elsevier, vol. 138(2), pages 513-531, June.
    12. Grendar, Marian & Judge, George G., 2006. "Large Deviations Theory and Empirical Estimator Choice," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt20n3j23r, Department of Agricultural & Resource Economics, UC Berkeley.

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