Bartlett Corrections Page

What is this page? This is a WWW home page for Bartlett corrections and their extensions. Such corrections were originally proposed by M.S. Bartlett in 1937 in an eventually influential paper entitled "Properties of sufficiency and statistical tests" published in the Proceedings of the Royal Society of London Series A. A general framework for Bartlett corrections was proposed by D.N. Lawley in a 1956 Biometrika paper.

What is plotted in the figure above? The figure above is a plot of the Bartlett-type correction to Rao's score statistic for a test involving the parameter of a von Mises distribution as a function of the this parameter (theta) and of the score statistic (S).

What are Bartlett corrections? Strictly speaking, a Bartlett correction is a scalar transformation applied to the likelihood ratio (LR) statistic that yields a new, improved test statistic which has a chi-squared null distribution to order O(1/n). This represents a clear improvement over the original statistic in the sense that LR is distributed as chi-squared under the null hypothesis only to order O(1).

Are there extensions of Bartlett corrections? Yes. Some of them arose in response to Sir David Cox's 1988 paper, "Some aspects of conditional and asymptotic inference: a review" (Sankhya A). A particularly useful one was proposed by Gauss Cordeiro and Silvia Ferrari in a 1991 Biometrika paper. They have shown how to Bartlett-correct test statistics whose null asymptotic distribution is chi-squared with special emphasis on Rao's score statistic.

Where can I find a survey paper on Bartlett corrections? There are a few around. Two particularly useful ones are:

What are the alternatives to Bartlett corrections? There are several alternatives. A closely related one are Edgeworth expansions, named after the economist/statistician Francis Ysidro Edgeworth. There are also saddlepoint expansions. A computer-intensive alternative is known as the bootstrap and was proposed by Bradley Efron in his 1979 Annals of Statistics paper.

Who is working on Bartlett corrections? There are a number of econometricians and statisticians working on this area. Here are some of them: C.L.F. Attfield, Reinaldo Arellano-Valle, Elisete Aubin, O.E. Barndorff-Nielsen, Lúcia Barroso, Denise Botter, T.K. Chandra, Andrew Chesher, Gauss Cordeiro, Francisco Cribari-Neto (i.e., me), Sir David Cox, Anthony Davison, Thomas DiCiccio, Silvia Ferrari, J.K. Ghosh, Peter Hall, J.L. Jensen, Fernando Lucambio, Peter McCullagh, Rahul Mukerjee, Bent Nielsen, Nancy Reid, Richard Smith, Richard Spady, Miguel Uribe-Opazo, Klaus Vasconcellos, Andrew T.A. Wood. (Please, do not flame me if I forgot to include some names here!...)

Which journals have had the greatest impact on the area? Most of the influential papers on Bartlett corrections were probably published in Biometrika. A number of other important papers appeared in the Annals of Statistics and in the Journal of the Royal Statistical Society B.

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"If those whose names we rescue from oblivion could be consulted they might tell us they would prefer to remain unknown." --Mathew Whiteford

Last revised on July 1, 2009 by Francisco Cribari-Neto.

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