This talk gives an overview on the nonparametric techniques that are useful for financial econometrics. The problems include estimation and inferences of instantaneous returns and volatility functions, time-dependent stochastic models, estimation of transition densities and state price densities. We first briefly describe the problems and then outline main techniques and main results. In particular, we will discuss in detail the new development on the dynamically integrating the time- and state-domain methods for volatility estimation. The former predominantly uses the data in the recent history while the latter mainly rely on historical information. Motivated by a study of the Bayesian estimation of volatility, we propose to estimate the volatility via dynamically integrating information from both the time and the state domains. The estimators from both domains are optimally combined based on a data driven weighting strategy, which results in several more efficient estimators. Some useful probabilistic aspects of diffusion processes are also briefly summarized to facilitate our presentation and applications.

One of central questions in genetic epidemiology is how to locate the susceptibility genes for diseases. In this regard, the traditional affected sibpair design has been and continues to be a popular approach to help investigators to narrow the chromosomal regions. This information will in turn be useful for fine mapping by carrying out association studies, either family-based or population-based, with a considerably larger number of SNPs. In this talk, by building upon the earlier work of Liang, Chiu and Beaty (Human Heredity, 2001), we discuss how this method maybe expanded to dealing with complex diseases, which face challenging issues including, among others, gene-gene interaction, genetic heterogeneity, imprinting, etc. These issues along with the proposed methods will be illustrated through genetic studies of asthma, schizophrenia and bipolar disorder, some of which are ongoing.

Two methods of model selection are discussed for change-point like problems, especially those arising in genetic linkage analysis.

The first is a method that selects the model with the smallest p-value, while the second is a modification of the Bayes Information Criterion (BIC). The methods are compared theoretically and on examples from the literature. For these examples, they are roughly comparable although the p-value based method is somewhat more liberal in selecting a high dimensional model.