Zongwu Cai
Department of Mathematics
University of North Carolina - Charlotte
Nonlinear Markov Regression Models with Application to Longitudinal Data
In this talk, first I will review Markov regression models in the
literature. Secondly, I propose a local quasi-likelihood approach to
regression analysis with discrete longitudinal data. In particular, I
consider a class of nonlinear time series models -functional-coefficient
models, which extend the Markov regression models for time series proposed
by Zeger and Qaqish (1988, Biometrics). The method I used to estimate the
coefficient functions is a local linear fitting technique and the asymptotic
property of the estimator is studied so that a consistent estimator of the
asymptotic variance can be derived. A nonparametric version of Akaike
information criterion is proposed to select the optimal bandwidth and the
best model. A simulated example and a real dataset for respiratory disease
are reported to illustrate the methodology.
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