**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:

- 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.

**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.

**Econometrics Links:**

- Durham Statistics Group
- Econometrics at the University of Illinois
- A Guide to Statistical Computing Resources on the Internet
- Midwest Econometrics Group (MEG)
- Society for Nonlinear Dynamics and Econometrics
- StatLib
- Wavelets Page

**Journals:**

- Biometrika
- Brazilian Journal of Probability and Statistics
- Computational Statistics
- Computational Statistics and Data Analysis
- Economics Letters
- Econometric Reviews
- Econometric Theory
- InterStat (electronic journal)
- Journal of Applied Econometrics
- Journal of Econometrics
- Journal of Statistical Planning and Inference
- Journal of Statistics Education
- Statistics and Computing
- Statistics and Probability Letters
- Studies in Nonlinear Dynamics and Econometrics

"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.

Send comments and suggestions to cribari@de.ufpe.br