Corrected maximum likelihood estimators in heteroscedastic symmetric nonlinear models

Journal of Statistical Computation and Simulation

Volumn 80, Issue 4, 2010, Pages 451-461

  Cysneiros, F J A ^a   Cordeiro, G M ^b   Cysneiros, A H M A ^a  

^a FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

^b UNIVERSIDADE FEDERAL RURAL DE PERNAMBUCO   (Brazil)

Author keywords

Bias correction; Heteroscedastic regression; Nonlinear model; Symmetric distribution

Indexed keywords

EID: 77951157565     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949650802706420     Document Type: Article

References (34)

1. I.F. Blake and J.B. Thomas, On class of processes arising in linear estimation theory, IEEE Trans. Inform. Theory 14 (1968), pp. 12-16.
2. D.K. McGraw and J.F. Wagner, Elliptically symmetrical distributions, IEEE Trans. Inform. Theory 14 (1968), pp. 110-120.
3. K.L. Lange, R.J.A. Little, and J.M.G Taylor, Robust statistical modelling using the t distribution, J. Amer. Statist. Assoc. 84 (1989), pp. 881-896.
4. J. Taylor and A. Verbyla, Joint modelling of location and scale parameter of the t distribution, Statist. Modelling 4 (2004), pp. 91-112.
5. M.A. Chmielewski, Elliptically symmetric distributions: A review and bibliography, Int. Statist. Rev. 49 (1981), pp. 67-74.
6. S. Cambanis, S. Huang, and G. Simons, On the theory of elliptically contoured distributions, J. Multivariate Anal. 11 (1981), pp. 368-385.
7. K.T. Fang, S. Kotz, and K.W. Ng, Symmetric Multivariate and Related Distributions, Chapman and Hall, London, 1990.
8. M. Galea, G.A. Paula, and H. Bolfarine, Local influence in elliptical linear regression models, Statistician 46 (1997), pp. 71-79.
9. S.Z. Liu, On local influence for elliptical linear models, Statist. Papers 41 (2000), pp. 211-224.
10. M. Galea, M. Riquelme, and G.A. Paula, Diagnostics methods in elliptical linear regression models, Braz. J. Probab. Statist. 14 (2000), pp. 167-184.
11. M. Galea, G.A. Paula and F.J.A. Cysneiros, On diagnostic in symmetrical nonlinear models, Statist. Probab. Lett. 73 (2005), pp. 459-467.
12. F.J.A. Cysneiros, G.A. Paula and M. Galea, Heteroscedastic symmetrical linear models, Statist. Probab. Lett. 77 (2007), pp. 1084-1090.
13. R.E. Park, Estimating with heteroscedastic terms, Econometrika 34 (1966), p. 888.
14. A.C. Harvey, Estimating regression models with multiplicative heteroscedasticity, Econmetrika 41 (1976), pp. 461-465.
15. A.C.Atkinson, Two graphical display for outlying and influential observations in regression, Biometrika 68 (1981), pp. 13-20.
16. R.D. Cook and S. Weisberg, Diagnostics for heteroscedasticity in regression, Biometrika 70 (1983), pp. 1-10.
17. G.K. Smyth, Generalized linear models with varying dispersion, J. R. Statist. Soc. Ser. B 51 (1989), pp.47-60.
18. D.A. Botter and G.M. Cordeiro, Improved estimators for generalized linear models with dispersion covariates, J. Statist. Comp. Simul. 62 (1998), pp. 91-104.
19. L.P. Barroso, G.M. Cordeiro, and K.L.P. Vasconcellos, Second-order asymptotic for score tests in heteroskedastict regression models, Comm. Statist. Theory Methods 31 (2002), pp. 1515-1529.
20. D. Kelker, Distribution theory of spherical distribution and a location-scale parameter generalization, Sankhya 32 (1970), pp. 419-430.
21. G.M. Cordeiro, S.L.P. Ferrari, M.A. Uribe-Opazo, and K.L.P. Vasconcellos, Corrected maximum-likelihood estimation in a class of symmetric nonlinear regression models, Statist. Probab. Lett. 46 (2000), pp. 317-328.
22. F.J.A. Cysneiros and G.A. Paula, Restricted methods in symmetrical linear models, Comput. Statist. Data Anal. 49 (2005), pp. 689-708.
23. B. Jørgensen, The delta algorithm and GLIM, Int. Statist. Rev. 52 (1984), pp. 283-300.
24. D.R. Cox and D.V. Hinkley, Theoretical Statistics. Chapman and Hall, London, 1974.
25. D.R. Cook, C.L. Tsai, and B.C. Wei, Bias in nonlinear regression, Biometrika 73 (1986), pp. 615-623.
26. G.M. Cordeiro and P. McCullagh, Bias correction in generalized linear models, J. R. Statist. Soc. Ser. B 53 (1991), pp. 629-643.
27. G.M. Cordeiro, Bartlett corrections and bias correction for two heteroscedastic regression models, Comm. Statist. Theory Methods 22 (1993), pp. 169-188.
28. K.L.P. Vasconcellos and S.G. Silva, Corrected estimates for Student t regression models with unknown degrees of freedom, J. Statist. Comp. Simul. 75 (2005), pp. 409-423.
29. R. Ospina, F. Cribari-Neto, and K.L.P Vasconcellos, Improved point and interval estimation for a beta regression model, Comput. Statist. Data Anal. 51 (2006), pp. 960-981.
30. G.M. Cordeiro, Corrected maximum likelihood estimators in linear heteroscedastic regression models, Braz. Rev. Econom. 28 (2008), pp. 53-67.
31. D.R. Cox and E.J. Snell, A general definition of residuals, J. R. Statist. Soc. Ser. B 30 (1968), pp. 248-275.
32. G.M. Cordeiro and G.A. Paula, Improved likelihood ratio statistics for exponential family nonlinear models, Biometrika 70 (1989), pp. 269-274.
33. G.M. Cordeiro and L.P. Barroso, A third-order bias corrected estimate in generalized linear models, Test 16 (2007), pp. 76-89.
34. J.A. Doornik, An Object-Ooriented Matrix Programming Language, 4th ed., Timberlake Consultants, London, Oxford, 2001; software avaliable at http://www.doornik.com.