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The Optimal Size of a Preliminary Test of Linear Restriction in a Mis-Specified Regression Model

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  • Giles, David E. A.
  • Lieberman, Offer
  • Giles, Judith A.

Abstract

When the choice of estimator for the coefficients in a linear regression model is determined by the outcome of a prior test of the validity of restrictions on the model, Brook (1976) has shown that a mini-max (risk) regret criterion leads to the simple rule that the optimal critical value for the preliminary test is approximately two in value, regardless of the degrees of freedom. We show that this result no longer holds in the (likely) event that relevant regressors are excluded from the model at the outset.

Suggested Citation

  • Giles, David E. A. & Lieberman, Offer & Giles, Judith A., "undated". "The Optimal Size of a Preliminary Test of Linear Restriction in a Mis-Specified Regression Model," Department of Economics Discussion Papers 262939, University of Canterbury - New Zealand.
    • Handle: RePEc:ags:canzdp:262939
    DOI: 10.22004/ag.econ.262939
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    References listed on IDEAS

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    1. Toyoda, T. & Wallace, T. D., 1975. "Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test," Journal of Econometrics, Elsevier, vol. 3(4), pages 395-404, November.
    2. Sawa, Takamitsu & Hiromatsu, Takeshi, 1973. "Minimax Regret Significance Points for a Preliminary Test in Regression Analysis," Econometrica, Econometric Society, vol. 41(6), pages 1093-1101, November.
    3. Toyoda, Toshihsa & Wallace, T D, 1976. "Optimal Critical Values for Pre-Testing in Regression," Econometrica, Econometric Society, vol. 44(2), pages 365-375, March.
    4. Giles, David E. A. & Clarke, Judith A., 1989. "Preliminary-test estimation of the scale parameter in a mis-specified regression model," Economics Letters, Elsevier, vol. 30(3), pages 201-205, September.
    5. 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.
    6. King, M.L. & Giles, D.E.A., 1984. "Autocorrelation pre-testing in the linear model: Estimation, testing and prediction," Journal of Econometrics, Elsevier, vol. 25(1-2), pages 35-48.
    7. Giles, David E. A., 1986. "Preliminary-test estimation in mis-specified regressions," Economics Letters, Elsevier, vol. 21(4), pages 325-328.
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