Robust Estimation and Selection for Semi-Varying Coefficient Models

Abstract

Varying coefficient models have gained popularity in recent years due to their exibility in modeling more realistic problems. On the other hand, parametric models provide better interpretability. Model selection can be performed for both types of models. This dissertation is focused on estimation and variable selection for a semiparametric combination of the two types of models known as the semi-varying coefficient model. This model provides a exible way to deal with various problems including problems that require spatiotemporal models. The approach used in this dissertation is based on rank estimation which provides a good balance between robustness and efficiency. First, we consider a rank-based estimation of the varying coe cient functions for semivarying coefficient model. The consistency and asymptotic normality of the proposed estimators are established. An extensive Monte-Carlo simulation study demonstrates the robustness and the efficiency of the proposed estimators compared to the least squares estimators. A back tting algorithm is developed for estimating the parametric and nonparametric parts of the model in alternate steps. The semi-varying coefficient model was motivated by the popular COVID-19 where the rank-based estimation is used to provide accurate estimates of factors affecting the mortality rate. We use a real data example to show that the classical approach is highly affected by outliers in response space but not the rank-based method we propose in this dissertation. This is followed by variable selection method for semi-varying coefficient model. We develop a LASSO-type rank-based variable selection procedure to select and estimate coefficient functions.