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Bartlett Corrections for One-Parameter Exponential Family Models


  • G.M. Cordeiro

    (Univ. Federal de Pernambuco)

  • F. Cribari-Neto

    (Southern Illinois Univ. at Carbondale)

  • E.C.Q. Aubin

    (Univ. de Sao Paulo)

  • S.L.P. Ferrari

    (Univ. de Sao Paulo)


In this paper we derive a general closed-form expression for the Bartlett correction for the test of H_0: \theta= \theta**(0), where "theta is a scalar parameter of a one-parameter exponential family model. Our results are general enough to cover many important and commonly used distributions. Several special cases and classes of variance functions of considerable importance are discussed, and some approximations based on asymptotic expansions are given. We also use a graphical analysis to examine how the correction varies with \theta in some special cases. Simulation results are also given.

Suggested Citation

  • 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, EconWPA.
  • Handle: RePEc:wpa:wuwpem:9506001
    Note: 20 pages; 10 self-contained figures and 3 tables; written with an implementation of TeX; single PostScript file FTP'ed. E-mail to Francisco Cribari-Neto (cribari @

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    References listed on IDEAS

    1. Cordeiro, Gauss M., 1993. "General matrix formulae for computing Bartlett corrections," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 11-18, January.
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    Cited by:

    1. 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.

    More about this item


    Bartlett correction; chi-squared distribution; exponential family; likelihood ratio statistic;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs


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