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A semi-parametric basis for combining estimation problems under quadratic loss

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Author Info

  • Judge, George G.

    ()
    (University of California, Berkeley. Dept of agricultural and resource economics and policy)

  • Mittelhammer, Ronald 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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Bibliographic Info

Paper provided by University of California at Berkeley, Department of Agricultural and Resource Economics and Policy in its series CUDARE Working Paper Series with number 948.

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Length: 30 pages
Date of creation: 2003
Date of revision:
Handle: RePEc:are:cudare:948

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Related research

Keywords: bootstrapping; estimation theory; linear models; multivariate analysis;

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References

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  1. 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.
  2. 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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Citations

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Cited by:
  1. 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.
  2. 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.
  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 & Cardell, Nicholas Scott, 2005. "Minimum divergence moment based binary response models : estimation and inference," CUDARE Working Paper Series 0998, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.
  5. 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.
  6. 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).
  7. Judge, George G. & Mittelhammer, Ronald C, 2004. "Estimating the link function in multinomial response models under endogeneity and quadratic loss," CUDARE Working Paper Series 0970, University of California at Berkeley, Department of Agricultural and Resource Economics and Policy.

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