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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :49-62    DOI: 10.1007/s10255-012-0123-0
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Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR(1) Errors
Chun-Zheng CAO1,2, Jin-Guan LIN2
1. College of Math & Physics, Nanjing University of Information Science & Technology, Nanjing 210044, China;
2. Department of Mathematics, Southeast University, Nanjing 210096, China
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Abstract The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.  
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Keywordsautocorrelation   elliptical distributions   heteroscedasticity   longitudinal data   nonlinear model   score test     
Abstract: The aim of this paper is to study the tests for variance heterogeneity and/or autocorrelation in nonlinear regression models with elliptical and AR(1) errors. The elliptical class includes several symmetric multivariate distributions such as normal, Student-t, power exponential, among others. Several diagnostic tests using score statistics and their adjustment are constructed. The asymptotic properties, including asymptotic chi-square and approximate powers under local alternatives of the score statistics, are studied. The properties of test statistics are investigated through Monte Carlo simulations. A data set previously analyzed under normal errors is reanalyzed under elliptical models to illustrate our test methods.  
Keywordsautocorrelation,   elliptical distributions,   heteroscedasticity,   longitudinal data,   nonlinear model,   score test     
Received: 2008-11-19;
Fund:

Supported by the National Natural Science Foundation of China (No. 11171065 and NSFJSBK2011058).

Cite this article:   
.Heteroscedasticity and/or Autocorrelation Checks in Longitudinal Nonlinear Models with Elliptical and AR(1) Errors[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 49-62
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0123-0      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/49
 
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