Q: What are Bartlett corrections?
A: 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).
Q: Are there extensions of Bartlett corrections?
A: 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.
Q: Where can I find a survey paper on Bartlett corrections?
A: There are a few around. Two particularly useful ones are:
- Cribari-Neto, F. and Cordeiro, G.M. (1996) On Bartlett and Bartlett-type corrections. Econometric Reviews, 15, 339-367.
- Jensen, J.L. (1993) A historical sketch and some new results on the improved likelihood statistic. Scandinavian Journal of Statistics, 20, 1-15.
Q: What are the alternatives to Bartlett corrections?
A: 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.
Please refer to Bartlett Corrections Page.