Heteroscedasticity and/or autocorrelation checks in longitudinal nonlinear models with elliptical and AR(1) errors

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.

Semiparametric hierarchical model with heteroscedasticity

“…Other researchers employed Bayesian approaches [7,15] and quantile regression methods [29] to assess the heterogeneity of residual variances in mixed models and multilevel models. Cao and Lin [2] further studied the hypothesis test for variance heterogeneity and autocorrelation in longitudinal nonlinear models.…”