Rank-Based Methods for Single-Index Varying Coefficient Models

Abstract

The single-index varying coefficient model has received much attention due to its flexibility and interpretability in recent years. This dissertation is mainly concerned with the rank-based estimation and variable selection in single-index varying coefficient models. In the first part of this dissertation, we consider a rank-based estimation of the index parameter and the coefficient functions for single-index varying 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. The rank-based approach was motivated by a problem from fisheries ecology where it is used to provide accurate estimates of interspecies dependence along an environmental gradient. 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 proposed in this dissertation. The second part of this dissertation is based on variable selection method for single-index varying coefficient model. We develop a LASSO-type rank-based variable selection procedure to select and estimate coefficient functions. A Monte-Carlo simulation study shows that the proposed method is highly robust and efficient compared to least squares type approaches. Our method can be easily applied to single-index and varying coefficient models since they are special cases of single-index varying coefficient model.