A Semiparametric Approach to Dual Modeling

In typical normal theory regression, the assumption of homogeneity of variances is often not appropriate. When heteroscedasticity exists, instead of treating the variances as a nuisance and transforming away the heterogeneity, the structure of the variances may be of interest and it is desirable to model the variances. Modeling both the mean and variance is commonly referred to as dual modeling. In parametric dual modeling, estimation of the mean and variance parameters are interrelated. When one or both of the models (the mean or variance model) are misspecified, parametric dual modeling can lead to faulty inferences. An alternative to parametric dual modeling is nonparametric dual modeling. However, nonparametric techniques often result in estimates that are characterized by high variability and ignore important knowledge that the user may have regarding the process. We develop a dual modeling approach [Dual Model Robust Regression (DMRR)], which is robust to user misspecification of the mean and/or variance models. Numerical and asymptotic results illustrate the advantages of DMRR over several other dual model procedures.