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Estimation of error variance in one-way random model

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Abstract

A preliminary-test estimator for the error variance in the one-way random model is considered. The optimum levels of significance for the preliminary test are obtained based on a regret function. A pooling procedure for estimating the error variance, based on weighting functions, is also considered. A comparison of these estimators is made.

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References

  • Bancroft TA (1944) On biases in estimation due to the use of preliminary tests of significance. Annals of Mathematical Statistics 15:190–204

    MathSciNet  MATH  Google Scholar 

  • Bancroft TA, Han C-P (1977) Inference based on conditional specification: A note and a bibliography. International Statistical Review 45:117–127

    MATH  MathSciNet  Google Scholar 

  • Brook RJ (1976) On the use of a regret function to set significance points in prior tests of estimation. Journal of the American Statistical Association 71:126–131

    Article  MATH  MathSciNet  Google Scholar 

  • Chiou P (1987) A preliminary test estimator of reliability in a life-testing model. IEEE Transactions on Reliability R-36:408–410

    Article  Google Scholar 

  • Chiou P (1988) Shrinkage estimation of scale parameter of the extreme-value distribution. IEEE Transactions on Reliability 37:370–374

    Article  MATH  Google Scholar 

  • Chiou P (1990) Estimation of scale parameters for two exponential distributions. IEEE Transactions on Reliability 39:106–109

    Article  MATH  Google Scholar 

  • Chiou P (1992) Shrinkage estimation of reliability in the exponential distribution. Communications in Statistics: Theory and Methods 21:1745–1758

    MATH  MathSciNet  Google Scholar 

  • Chiou P, Han C-P (1989) Shrinkage estimation of threshold parameter of the exponential distribution. IEEE Transactions on Reliability 38:449–453

    Article  MATH  Google Scholar 

  • Giles DEA, Lieberman O, Giles JA (1992) The optimal size of a preliminary test of linear restrictions in a misspecified regression model. Journal of the American Statistical Association 87:1153–1157

    Article  Google Scholar 

  • Gradshteyn IS, Ryzhik IM (1980) Table of Integrals, Series, and Products. New York Academic Press Inc

    MATH  Google Scholar 

  • Han C-P (1978) Nonnegative and preliminary test estimators of variance components. Journal of the American Statistical Association 73:855–858

    Article  MATH  MathSciNet  Google Scholar 

  • Han C-P, Rao CV, Ravichandran J (1988) Inference based on conditional specification: A second bibliography. Communications in Statistics-Theory and Methods 17:1945–1964

    MATH  MathSciNet  Google Scholar 

  • Huntsberger DV (1955) A generalization of a preliminary testing procedure for pooling data. Annals of Mathematical Statistics 26:734–743

    MathSciNet  Google Scholar 

  • Ohtani K, Toyoda T (1978) Minimax regret critical values for a preliminary test in pooling variances. Journal of the Japan Statistical Society 8:15–20

    MathSciNet  Google Scholar 

  • Sawa T, Hiromatsu T (1973) Minimax regret significance points for a preliminary test in regression analysis. Econometrica 41:1093–1101

    Article  MATH  Google Scholar 

  • Singh J (1971) Pooling mean squares. Journal of the American Statistical Association 66:82–85

    Article  MATH  Google Scholar 

  • Srivastava SR (1972) Pooling mean squares in ANOVA model II. Journal of the American Statistical Association 67:676–679

    Article  MATH  Google Scholar 

  • Toyoda T, Wallace TD (1975) Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test. Journal of Econometrics 3:395–404

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Lamar University, 77710, Beaumont, Texas, USA

    Paul Chiou

  2. Department of Mathematics, University of Texas at Arlington, 76019, Arlington, Texas, USA

    Chien-Pai Han

Authors
  1. Paul Chiou
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  2. Chien-Pai Han
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Chiou, P., Han, CP. Estimation of error variance in one-way random model. Metrika 44, 41–51 (1996). https://doi.org/10.1007/BF02614053

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