NONPARAMETRIC ESTIMATION OF CONDITIONAL VARIANCE AND COVARIANCE FUNCTIONS

Abstract

In recent times, estimation of the conditional covariance matrix has received much attention in many areas. Even though several statistical models have been introduced to avoid the curse of dimensionality problem, those models still have limited capability to describe different patterns of dependence in the data. In this thesis, we study this estimation problem through two aspects. First, to study the correlation structure for a portfolio of financial assets, we explore the effect of the exogenous variable on pairwise correlations by utilizing a reduced rank model. The second problem considered is how to efficiently estimate conditional variance (covariance) functions. Instead of estimating the mean function at the first stage, we propose a novel approach by combining the techniques in kernel smoothing and difference-based method, which outperforms two existing approaches in most cases. Furthermore, we provide a detailed theoretical justification, including consistency and asymptotic normality of our proposed estimators.