Nearly unbiased estimation in a biparametric exponential family

References

• Box , M. 1971 . Bias in nonlinear estimation (with discussion) . Journal of the Royal Statistical Society B , 33 : 171 – 201 .
   Google Scholar
• Pike , M. , Hill , A. and Smith , P. 1980 . Bias and efficiency in logistic analysis of stratified case-control studies . International Journal of Epidemiology , 9 : 89 – 95 .
   PubMed Web of Science ®Google Scholar
• Cook , R. , Tsai , C. and Wei , B. 1986 . Bias in nonlinear regression . Biometrika , 73 : 615 – 623 .
   Web of Science ®Google Scholar
• Young , D. and Bakir , S. 1987 . Bias correction for a generalized log-gamma regression model . Technometrics , 29 : 183 – 191 .
   Web of Science ®Google Scholar
• Cordeiro , G. M. and McCullagh , P. 1991 . Bias correction in generalized linear models . Journal of the Royal Statistical Society B , 53 : 629 – 643 .
   Google Scholar
• Firth , D. 1993 . Bias reduction of maximum likelihood estimates . Biometrika , 80 : 27 – 38 .
   Web of Science ®Google Scholar
• Cordeiro , G. M. and Vasconcellos , K. L.P. 1997 . Bias correction for a class of multivariate nonlinear regression models . Statistics and Probability Letters , 35 : 155 – 164 .
   Google Scholar
• Cordeiro , G. M. and Vasconcellos , K. L.P. 1999 . Second-order biases of the maximum likelihood estimates in von Mises regression models . Australian and New Zealand Journal of Statistics , 41 : 901 – 910 .
   Web of Science ®Google Scholar
• Cribari–Neto , F. and Vasconcellos , K. L.P. 2002 . Nearly unbiased maximum likelihood estimation for the beta distribution . Journal of Statistical Computation and Simulation , 72 : 107 – 118 .
   Web of Science ®Google Scholar
• Vasconcellos , K. L.P. and Cribari-Neto , F. 2005 . Improved maximum likelihood estimation in a new class of beta regression models . Brazilian Journal of Probability and Statistics , 19 : 13 – 31 .
   Google Scholar
• Vasconcellos , K. L.P. and Silva , S. G. 2005 . Corrected estimates for Student t regression models with unknown degrees of freedom . Journal of Statistical Computation and Simulation , 75 : 409 – 423 .
   Web of Science ®Google Scholar
• Vasconcellos , K. L.P. , Frery , A. C. and Silva , L. B. 2005 . Improving estimation in speckled imagery . Computational Statistics , 20 : 503 – 519 .
   Web of Science ®Google Scholar
• Lindsay , B. G. 1986 . Exponential family mixture models . The Annals of Statistics , 14 : 124 – 137 .
   Web of Science ®Google Scholar
• Gelfand , A. E. and Dalal , S. R. 1990 . A note on overdispersed exponential families . Biometrika , 77 : 55 – 64 .
   Web of Science ®Google Scholar
• Dey , D. K. , Gelfand , A. E. and Pen , F. 1997 . Overdispersed generalized linear models . Journal of Statistical Planning and Inference , 64 : 93 – 107 .
   Web of Science ®Google Scholar
• Cox , D. R. and Hinkley , D. 1974 . Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• Lawley , D. 1956 . A general method for approximating to the distribution of likelihood ratio criteria . Biometrika , 43 : 295 – 303 .
   Web of Science ®Google Scholar
• Doornik , J. A. 2001 . Ox: an Object-oriented Matrix Programming Language , 4 , London : Timberlake Consultants and Oxford . Available online at: //www.doornik.com
   Google Scholar
• Fletcher , R. 1987 . Practical Methods of Optimization , New York : John Wiley and Sons .
   Google Scholar
• Cox , D. and Snell , E. 1968 . A general definition of residuals . Journal of the Royal Statistical Society B , 30 : 248 – 275 .
   Google Scholar
• Wolfram , S. 1991 . Mathematica: a System for Doing Mathematics by Computer , Massachusets : Addison-Wesley .
   Google Scholar
• Abell , M. L. and Braselton , J. P. 1994 . The Maple V Handbook , New York : AP Professional .
   Google Scholar
• Efron , B. and Tibshirani , R. J. 1993 . An Introduction to the Bootstrap , New York : Chapman and Hall .
   Google Scholar
• Chhikara , R. S. and Folks , J. L. 1988 . The Inverse Gaussian Distribution (Theory, Methodology and Applications) , New York : Marcel Dekker .
   Google Scholar
• Seshadri , V. 1998 . The Inverse Gaussian Distribution: Statistical Theory and Applications (Lecture Notes in Statistics) , (Springer)
   Google Scholar
• Johnson , N. L. , Kotz , S. and Balakrishnan , N. 1995 . Continuous Univariate Distributions , Vol. 2 , New York : John Wiley .
   Google Scholar
• Florens , J. P. , Mouchart , M. and Rolin , J. M. 1999 . Semi and non parametric Bayesian analysis of duration models: a survey . International Statistical Review , 67 : 187 – 210 .
   Web of Science ®Google Scholar
• Jones , M. C. 2004 . Families of distributions arising from distributions of order statistics (with discussion) . Test (Sociedad Española de Estádística e Investigación Operativa) , 13 ( 1 ) : 1 – 43 .
   Google Scholar
• Dufresne , D. 2005 . “ Fitting combinations of exponentials to probability distributions ” . Australia : Department of Economics, University of Melbourne . Working paper 121
   Google Scholar
• Hu , P. , Greenwood , C. and Beyene , J. 2005 . Integrative analysis of multiple gene expression profiles with quality-adjusted effect size models . BMC:Bioinformatics , 6 : 128 Available online at: // www.biomedcentral.com/1471-2105/6/128
   PubMed Web of Science ®Google Scholar