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General matrix formulae for computing Bartlett corrections

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  • Cordeiro, Gauss M.

Abstract

We give general formulae using matrix notation for computing Bartlett corrections for the likelihood ratio statistics in two quite distinct situations. In the first, we consider the test of a null hypothesis, which specifies a parameter vector, in the presence of nuisance parameters. In the second, we are interested in testing a scalar parameter which is orthogonal to the remaining nuisance parameters. The formulae have advantages for numerical purposes because they require only simple operations on matrices and vectors. They are also useful in connexion with algebraic computing packages to obtain closed-form Bartlett corrections in a variety of important problems. The practical use of such formulae is illustrated.

Suggested Citation

  • Cordeiro, Gauss M., 1993. "General matrix formulae for computing Bartlett corrections," Statistics & Probability Letters, Elsevier, vol. 16(1), pages 11-18, January.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:1:p:11-18
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    Citations

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    Cited by:

    1. Akimichi Takemura & Satoshi Kuriki, 1996. "A proof of independent Bartlett correctability of nested likelihood ratio tests," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 603-620, December.
    2. 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.
    3. Kakizawa, Yoshihide, 2011. "Improved additive adjustments for the LR/ELR test statistics," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1245-1255, August.
    4. 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.

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