Nonparametric Quasi-likelihood in Longitudinal Data Analysis
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This dissertation proposes a nonparametric quasi-likelihood approach to estimate regression coefficients in the class of generalized linear regression models for longitudinal data analysis, where the covariance matrices of the longitudinal data are totally unknown but are smooth functions of means. This proposed nonparametric quasi-likelihood approach is to replace the unknown covariance matrix with a nonparametric estimator in the quasi-likelihood estimating equations, which are used to estimate the regression coefficients for longitudinal data analysis. Local polynomial regression techniques are used to get the nonparametric estimator of the unknown covariance matrices in the proposed nonparametric quasi-likelihood approach. Rates of convergence of the resulting estimators are established. It is shown that the nonparametric quasi-likelihood estimator is not only consistent but also has the same asymptotic distribution as the quasi-likelihood estimator obtained with the true covariance matrix. The results from simulation studies show that the performance of the nonparametric quasi-likelihood estimator is comparable to other methods with given marginal variance functions and correctly specified correlation structures. Moreover, the results of the simulation studies show that nonparametric quasi-likelihood corrects some shortcomings of Liang and Zeger's GEE approach in longitudinal data analysis.