Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models

Statistics and Probability Letters

Volumn 46, Issue 4, 2000, Pages 317-328

  Cordeiro, Gauss M ^a   Ferrari, Silvia L P ^b   Uribe Opazo, Miguel A ^c   Vasconcellos, Klaus L P ^a  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b UNIVERSITY OF SÃO PAULO   (Brazil)

^c Departamento de Matemíatica e Estatística   (Brazil)

Author keywords

Bias correction; Maximum likelihood estimate; Nonlinear regression; Symmetric distribution* t distribution

Indexed keywords

EID: 0041777871     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(99)00118-2     Document Type: Article

References (34)

1. Abell, M.L., Braselton, J.P., 1994. The MAPLE V Handbook. AP Professional, New York.
2. Albert J., Delampady M., Polasek W. A class of distributions for robustness studies. J. Statist. Planning Inference. 28:1991;291-304.
3. Berkane M., Bentler P.M. Moments of elliptically distributed random variates. Statist. Probab. Lett. 4:1986;333-335.
4. Blake I.F., Thomas J.B. On class of processes arising in linear estimation theory. IEEE. Trans. Info. Theory. 14:1968;12-16.
5. Box, G.E.P., Tiao, G.C., 1973. Bayesian Inference in Statistical Analysis. Addison-Wesley, London.
6. Cambanis S., Huang S., Simons G. On the theory of elliptically contoured distributions. J. Multivariate Anal. 11:1981;368-385.
7. Chmielewski, M.A., 1981. Elliptically symmetric distributions: a review and bibliography. Internat. Statist. Rev. 49, 67-74.
8. Chu K. Estimation and decision for linear systems with elliptical random processes. IEEE. Trans. Automat. Control. 18:1973;499-505.
9. Cook D.R., Tsai C.L., Wei B.C. Bias in nonlinear regression. Biometrika. 73:1986;615-623.
10. Cordeiro G.M., Klein R. Bias correction in ARMA models. Statist. Probab. Lett. 19:1994;169-176.
11. Cordeiro G.M., McCullagh P. Bias correction in generalized linear models. J. Roy. Statist. Soc. B. 53:1991;629-643.
12. Cordeiro, G.M., Paula, G.A., 1989. Fitting non-exponential family nonlinear models in GLIM by using the offset-facility, vol. 57. Lecture Notes in Statistics, pp. 105-114.
13. Cordeiro G.M., Vasconcellos K.L.P. Bias correction for a class of multivariate nonlinear regression models. Statist. Probab. Lett. 35:1997;155-164.
14. Cordeiro G.M., Vasconcellos K.L.P., Santos M.L.F. On the second-order bias of parameter estimates in nolinear regression models with Student. t errors J. Statist. Comput. Simulation. 60:1998;363-378.
15. Cox, D.R., Hinkley, D.V., 1974. Theoretical Statistics. Chapman & Hall, London.
16. Cox D.R., Snell E.J. A general definition of residuals (with discussion). J. Roy. Statist. Soc. B. 30:1968;248-278.
17. Darby S.C., Ellis M.J. A test for synergism between two drugs. J. Appl. Statist. 25:1976;296-299.
18. Fang, K.T., Kotz, S., NG, K.W., 1990. Symmetric Multivariate and Related Distributions. Chapman & Hall, London.
19. Gallant, A.R., 1975. Nonlinear Statistical Models. Wiley, New York.
20. Kelker D. Distribution theory of spherical distributions and a location-scale parameter generalization. Sankhyā 32:1970;419-430.
21. Kotz, S., 1975. Multivariate distributions at a cross-road. In: Patil G.P., Kotz, S., Ord, J.K., (Eds.), Statistical Distributions in Scientific Work, 1, pp. 247-270.
22. McCullagh, P., 1987. Tensor Methods in Statistics. Chapman & Hall, London.
23. McCullagh, P., Nelder, J.A., 1989. Generalized Linear Models. Chapman & Hall, London.
24. McGraw D.K., Wagner J.F. Elliptically symmetric distributions. IEEE. Trans. Inform. Theory. 14:1968;110-120.
25. Muirhead, R., 1980. The effects of symmetric distributions on some standard procedures involving correlation coefficients. In: Gupta R.P., (Ed.), Multivariate Statistical Analysis. North-Holland, Amsterdam, pp. 143-159.
26. Muirhead, R., 1982. Aspects of Multivariate Statistical Theory. Wiley, New York.
27. Paula G.A. Bias correction for exponential family nonlinear models. J. Statist. Comput. Simulation. 40:1992;43-54.
28. Paula G.A., Cordeiro G.M. Bias correction and improved residuals for non-exponential family nonlinear models. Commun. Statist. Simulation Comput. 24:1995;1193-1210.
29. Rao B.L.S.P. Remarks on univariate symmetric distributions. Statist. Probab. Lett. 10:1990;307-315.
30. Ratkowsky, D.A., 1983. Nonlinear Regression Modelling: A Unified Practical Approach. Marcel Dekker, New York (Statistics, Textbooks and Monographs, vol. 48).
31. Serfling, R.J., 1980. Approximation Theorems of Mathematical Statistics. Wiley, New York.
32. Stone M. Discussion of paper by D.M. Bater and D.G. Watts. J. Roy. Statist. Soc. B. 42:1980;17-19.
33. Young D.H., Bakir S.T. Bias correction for a generalized log-gamma regression model. Technometrics. 29:1987;183-191.
34. Wolfram, S., 1996. The Mathematica Book, 3rd Edition. Cambridge University Press, New York.