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The Restricted Least Squares Stein-Rule in gretl

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Listed:
  • Lee C. Adkins

    (Oklahoma State University)

Abstract

The paper documents a Gretl function package that is used for the Restricted Least Squares (RLS) Stein-rule estimator. Judge and Bock (1981, pp. 240-42) proposed a family of Stein-rule estimators that dominates the MLE of in the CNLRM under weighted quadratic loss. The estimator is a linear combination of the unrestricted and restricted MLEs, where the degree of shrinkage is controlled using a conventional Wald test of the implied hypothesis restrictions. The Gretl function computes the positive-part version of the RLS Stein-rule that allows users to specify the desired linear restrictions on the model and to select a loss function under which to compute the RLS-Stein rule. In the absence of specifi c prior information about parameter values Lindley's version of the James-Stein rule is particularly attractive; accordingly, it is off ered as a user speci fied option. The fi nal version of the paper will also provide options for computing bootstrap standard errors [see Adkins (1990); Adkins and Hill 1990a)]. A simple Monte Carlo simulation is performed to explore the risk characteristics of the RLS-Stein rule vs. those of pretest, restricted mle, and unrestricted mle. All of the computations are preformed in gretl.

Suggested Citation

  • Lee C. Adkins, 2013. "The Restricted Least Squares Stein-Rule in gretl," Economics Working Paper Series 1305, Oklahoma State University, Department of Economics and Legal Studies in Business.
    • Handle: RePEc:okl:wpaper:1305
    as

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    File URL: https://business.okstate.edu/site-files/docs/ecls-working-papers/OKSWPS1305.pdf
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    References listed on IDEAS

    as
    1. Mittelhammer, Ron C., 1985. "Quadratic risk domination of restricted least squares estimators via Stein-ruled auxiliary constraints," Journal of Econometrics, Elsevier, vol. 29(3), pages 289-303, September.
    2. Mittelhammer, R.C., 1984. "Restricted least squares, pre-test, ols and stein rule estimators: Risk comparisons under model misspecification," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 151-164.
    3. Brownstone, David, 1990. "Bootstrapping improved estimators for linear regression models," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 171-187.
    4. Lee C. Adkins & R. Carter Hill, 1990. "The RLS Positive-Part Stein Estimator," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 72(3), pages 727-730.
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    More about this item

    Keywords

    Shrinkage estimation; prior information; gretl;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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