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Improved score tests for one-parameter exponential family models

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  • Ferrari, Silvia L. P.
  • Cordeiro, Gauss M.
  • Uribe-Opazo, Miguel A.
  • Cribari-Neto, Francisco

Abstract

Under suitable regularity conditions, an improved score test was derived by Cordeiro and Ferrari (1991). The test is based on a corrected score statistic which has a chi-squared distribution to order n-1 under the null hypothesis, where n is the sample size. In this paper we follow their approach and obtain a Bartlett-corrected score statistic for testing Ho : [theta] = [theta](o), where [theta] is the scalar parameter of a one-parameter exponential family model. We apply our main result to a number of special cases and derive approximations for corrections that involve unusual functions. We also obtain Bartlett-type corrections for natural exponential families.

Suggested Citation

  • Ferrari, Silvia L. P. & Cordeiro, Gauss M. & Uribe-Opazo, Miguel A. & Cribari-Neto, Francisco, 1996. "Improved score tests for one-parameter exponential family models," Statistics & Probability Letters, Elsevier, vol. 30(1), pages 61-71, September.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:1:p:61-71
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    References listed on IDEAS

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    1. Ferrari, Silvia L. P. & Cordeiro, Gauss M., 1996. "Corrected score tests for exponential family nonlinear models," Statistics & Probability Letters, Elsevier, vol. 26(1), pages 7-12, January.
    2. Cordeiro, Gauss M., 1993. "General matrix formulae for computing Bartlett corrections," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 11-18, January.
    3. Mukerjee, Rahul, 1990. "Comparison of tests in the multiparameter case I. Second-order power," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 17-30, April.
    4. G.M. Cordeiro & F. Cribari-Neto & E.C.Q. Aubin & S.L.P. Ferrari, 1995. "Bartlett Corrections for One-Parameter Exponential Family Models," Econometrics 9506001, University Library of Munich, Germany.
    5. Takesi Hayakawa, 1977. "The likelihood ratio criterion and the asymptotic expansion of its distribution," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 29(1), pages 359-378, December.
    6. F. Cribari-Neto & G.M. Cordeiro, 1995. "On Bartlett and Bartlett-Type Corrections," Econometrics 9507001, University Library of Munich, Germany.
    7. Mukerjee, Rahul, 1990. "Comparison of tests in the multiparameter case II. A third-order optimality property of Rao's test," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 31-48, April.
    8. Cribari-Neto, Francisco & Zarkos, Spyros, 1995. "Improved test statistics for multivariate regression," Economics Letters, Elsevier, vol. 49(2), pages 113-120, August.
    9. Francisco Cribari-Neto & Spyros Zarkos, 1995. "Improved Test Statistics for Multivariate Regression," Econometrics 9506003, University Library of Munich, Germany.
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    Cited by:

    1. Erik Meijer & Jelmer Ypma, 2008. "A Simple Identification Proof for a Mixture of Two Univariate Normal Distributions," Journal of Classification, Springer;The Classification Society, vol. 25(1), pages 113-123, June.

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