Speaker: Yichao Wu,
Title: Local quasi-likelihood method with a parametric guide
Date: Tuesday, Feburary 19, 2008
Time:
Place: 552 Hill Center
Abstract
Generalized linear models and quasi-likelihood method extend the ordinary regression models to accommodate more general conditional distributions of the response. They are commonly used statistical methods in practice. Despite their popularity, the same deficiency of the parametric ordinary regression applies to parametric generalized linear models in the sense that misspecification of the parametric model can lead to a completely wrong picture of the underlying conditional mean function. In contrast, nonparametric methods need no explicit parametric specification and, as a result, are more flexible. The resulting model is completely determined by the data. However, nonparametric estimation schemes in general have slower convergence rates than the parametric methods. A typical example is the local polynomial estimation of nonparametric quasi-likelihood studied by Fan, Heckman, and Wand (1995).
In this work, we propose to combine parametric and nonparametric methods. Specifically, two parametrically guided nonparametric estimation schemes are proposed by incorporating some prior shape information into consideration. Asymptotic theory and numerical simulations are used to demonstrate their improvement over the original nonparametric method. The results show that, with a reasonable parametric guide, our new methods enjoy smaller bias than the original nonparametric method. A real application to financial data is discussed.
This is a joint work with Jianqing Fan and Yang Feng.