Testing serial correlation in partially linear additive models

Abstract

This thesis proposes procedures for testing serial correlation in the partially linear additive models without and with errors in variables, which include the partially linear models and additive models as their special cases. For the partially linear additive models without errors, an empirical-likelihood-based procedure is developed based on the profile least-squares method. It is shown that the proposed test statistic is asymptotically chi-square distributed under the null hypothesis of no serial correlation. Then the rejection region can be constructed using this result. It is noted that the procedures are not only for testing zero first-order serial correlation, but also for testing higher-order serial correlation. For the partially linear additive models with errors, the methods based on the profile least-squares is invalid because of the existence of the errors in variables. By a corrected profile least-squares approach, another empirical-likelihood-based procedure is developed. The asymptotic properties are investigated, based on which the rejection region can be easily constructed. Extensive simulation studies were conducted to assess the finite sample properties of the proposed procedures' sizes and powers.