Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors

References

• Aitkin , M. 1987 . Modelling variance heterogeneity in normal regression using GLIM . Appl. Stat. , 36 : 332 – 339 .
   Web of Science ®Google Scholar
• Aitkinson , A. and Riani , M. 2000 . Robust Diagnostic Regression Analysis , New York : Springer-Verlag .
   Google Scholar
• Barroso , L. P. and Coreiro , G. M. 2005 . Bartlett corrections in heteroskedastic t regression models . Statist. Probab. Lett. , 75 : 86 – 96 .
   Web of Science ®Google Scholar
• Bates , D. M. and Watts , D. G. 1989 . Nonlinear Regression Analysis and its Applications , New York : John Wiley & Sons .
   Google Scholar
• Brockwell , P. J. and Davis , R. A. 1991 . Time Series: Theory and Methods , 2 , New York : Springer-Verlag .
   Google Scholar
• Castillo-Freeman , A. J. and Freeman , R. B. 1992 . “ When the minimum wage really bites: The effect of the U.S. level minimum on Puerto Rico ” . In Immigration and the Work Force , Edited by: Borjas , G. J. and Freeman , R. B. 177 – 211 . Chicago : University of Chicago Press .
   Google Scholar
• Chen , C. F. 1983 . Score test for regression models . J. Am. Statist. Assoc. , 78 : 158 – 161 .
   Web of Science ®Google Scholar
• Cook , R. D. and Weisberg , S. 1983 . Diagnostics for heteroscedasticity in regression . Biometrika , 70 : 1 – 10 .
   Web of Science ®Google Scholar
• Cox , D. R. and Hinkley , D. V. 1974 . Theoretical Statistics , London : Chapman and Hall .
   Google Scholar
• Cox , D. R. and Reid , N. 1987 . Parameter orthogonality and approximate conditional inference . J. R. Statist. Soc. Ser. B , 49 ( 1 ) : 1 – 39 .
   Google Scholar
• Cysneiros , F. J.A. , Paula , G. A. and Galea , M. 2007 . Heteroscedasticitic symmetrical linear models . Statist. Probab. Lett. , 77 : 1084 – 1090 .
   Web of Science ®Google Scholar
• Epps , T. W. and Epps , M. L. 1977 . The robustness of some standard tests for autocorrelation and heteroscedasticity when both problems are present . Econometrica , 45 : 745 – 753 .
   Web of Science ®Google Scholar
• Fernandez , C. and Steel , M. F.J. 1999 . Multivariate Student-t regression models: Pitfalls and inference . Biometrika , 86 ( 1 ) : 153 – 167 .
   Web of Science ®Google Scholar
• Godfrey , L. G. 1978 . Testing against general autoregressive and moving average error models when the regressors include lagged dependence variables . Econometrica , 46 : 1293 – 1301 .
   Web of Science ®Google Scholar
• Harrison , M. J. and McCabe , B. P.M. 1975 . Autocorrelation with heteroscedasticity: A note on the robustness of Durbin-Watson, Geary and Henshaw tests . Biometrika , 62 : 214 – 216 .
   Web of Science ®Google Scholar
• Hutton , J. L. and Solomon , P. J. 1997 . Parameter orthogonality in mixed regression models for survival data . J. R. Statist. Soc. Ser. B , 59 ( 1 ) : 125 – 136 .
   Google Scholar
• Kotz , S. and Nadarajah , S. 2004 . Multivariate t Distributions and their Applications , Cambridge : Cambridge University Press .
   Google Scholar
• Lange , K. L. , Little , R. J.A. and Taylor , J. M.G. 1989 . Robust statistical modelling using the t distribution . J. Am. Statist. Assoc. , 84 : 881 – 896 .
   Web of Science ®Google Scholar
• Lin , J. G. and Wei , B. C. 2004 . Testing for heteroscedasticity and correlation in nonlinear regression with correlated errors . Comm. Statist. Theory Methods , 33 ( 2 ) : 251 – 275 .
   Web of Science ®Google Scholar
• Lin , J. G. and Wei , B. C. 2006 . Approximate power of score test for variance heterogeneity under local alternatives in nonlinear models . Comput. Statist. Data Anal. , 50 : 3179 – 3198 .
   Web of Science ®Google Scholar
• Lin , J. G. , Wei , B. C. and Zhang , N. S. 2004 . Varying dispersion diagnostics for inverse gaussian regression models . J. Appl. Stat. , 31 : 1157 – 1170 .
   Web of Science ®Google Scholar
• Lin , J. G. , Zhu , L. X. and Xie , F. C. 2009 . Heteroscedasticity diagnostics for t linear regression models . Metrika , 70 : 59 – 77 .
   Web of Science ®Google Scholar
• Liu , C. H. and Rubin , D. B. 1995 . ML estimation of the t distribution using EM and its extensions, ECM and ECME . Statist. Sinica , 5 : 19 – 39 .
   Web of Science ®Google Scholar
• Lubin , J. H. and Gail , M. H. 1990 . On power and sample size for studying features of the relative odds of disease . Am. J. Epidemiol. , 131 : 552 – 566 .
   PubMed Web of Science ®Google Scholar
• Nadarajah , S. and Kotz , S. 2006 . Percentage points of the multivariate t distribution . Int. Statist. Rev. , 74 ( 1 ) : 15 – 30 .
   Web of Science ®Google Scholar
• Self , S. G. and Mauritsen , R. 1988 . Power/sample size calculations for generalized linear models . Biometrics , 44 : 79 – 86 .
   Web of Science ®Google Scholar
• Self , S. G. , Mauritsen , R. and Ohara , J. 1992 . Power calculations for likelihood ratio tests in generalized linear models . Biometrics , 48 : 31 – 39 .
   Web of Science ®Google Scholar
• Simonoff , J. S. and Tsai , C. L. 1994 . Improved tests for nonconstant variance in regression based on the modified profile likelihood . Appl. Stat. , 43 : 357 – 370 .
   Web of Science ®Google Scholar
• Singh , R. K. 1988 . Estimation of error variance in linear regression models with errors having multivariate Student-t distribution with unknown degrees of freedom . Econom. Lett. , 27 : 47 – 53 .
   Web of Science ®Google Scholar
• Taylor , J. T. and Verbyla , A. P. 2004 . Joint modelling of location and scale parameters of the t distribution . Stat. Model. , 4 : 91 – 112 .
   Web of Science ®Google Scholar
• Tsai , C. L. 1986 . Score test for the first-order autoregressive model with heteroscedasticity . Biometrika , 73 : 455 – 460 .
   Web of Science ®Google Scholar
• Verbyla , A. P. 1993 . Modelling variance heterogeneity:residual maximum likelihood and diagnostics . J. R. Stat. Soc. Ser. B , 55 : 509 – 521 .
   Google Scholar
• Wei , B. C. , Shi , J. Q. , Fung , W. K. and Hu , Y. Q. 1998 . Testing for varying dispersion in exponential family nonlinear models . Ann. Inst. Statist. Math. , 50 : 277 – 294 .
   Web of Science ®Google Scholar
• White , H. 1980 . A heteroskedasticity consistent covariance matrix estimator and a direct test for heteroskedasticity . Econometrica , 48 : 817 – 838 .
   Web of Science ®Google Scholar
• Wooldridge , J. 2003 . Introductory Econometrics: A Modern Approach , Mason : Thomson South-Western .
   Google Scholar