Inferences for Multivariate Semiparametric and Nonparametric Models with Applications to Risk Management

Princeton University, Princeton NJ

Investigators

Abstract

Abstract PI: Jianqing Fan DMS-0204329 The objectives of this proposal are to develop new and widely applicable approaches for semiparametric and nonparametric estimation and inferences, to study theoretical properties of these new approaches, and to evaluate their efficacy in data analyses. This proposal not only introduces a number of innovative techniques, but also provides various new and deep insights into statistical foundation. It will have significant impact on the future research of statistical methodologies, computation and theories. In particular, three inter-related areas are proposed for study. Firstly, a family of flexible semiparametric and nonparametric models is introduced. This allows one to study the extent to which response variables are associated with their covariates. The generalized likelihood ratio statistics is proposed for testing various hypotheses in multivariate semiparametric and nonparametric models. Secondly, new semiparametric and nonparametric models are proposed for understanding interest-rate dynamics, and stock price volatilities. Furthermore, the information on state-domain is incorporated to improve the efficiency of volatility estimation for bonds and to more accurately estimate the market risks of a portofolio. Thirdly, new techniques for variable selection, in the presence of a large number of variables, are proposed via nonconcave penalized likelihood. The innovation is that they estimate parameters and select variables simultaneously. The above techniques are widely applicable to many scientific and engineering problems. Multivariate nonparametric, semiparametric and large parametric models have been widely used. Statistical questions often arise such as if certain variables or factors are important to public health; if some risk factors contribute significantly to the survival time of patients; and if interest-rate dynamics or stock price processes are time-dependent or follow certain famous hypotheses, among others. Yet, there are no generally applicable tools available to answer these questions in multivariate semiparametric and non-saturated nonparametric models. The techniques proposed here permit one to objectively test scientific hypotheses without restrictive model assumptions. The techniques allow to better price financial derivatives and manage investment risk, to identify important risk variables and their possible interactions in the analysis of large epidemiological studies and to scrutinize famous hypotheses on stock prices