Some classical and Bayesian nonparametric regression methods in a longitudinal marginal model
We consider nonparametric regression in longitudinal data with dependence within subjects. The object is to estimate the unknown true function at a given point. Both classical and Bayesian approaches are studied.
In classical statistics, the local polynomial kernel method for longitudinal data possesses a somewhat surprising phenomenon called working independence, which implies this common classical method fails to use the correlations inherent in longitudinal data. Motivated by this interesting but somewhat inexplicable phenomenon, we develop a new two-stage kernel method that is carefully designed to utilize the correlation structure.
For Bayesian analysis of longitudinal data, we develop two nonparametric Bayesian regression methods using two prior structures, which are the Dirichlet process mixtures and the Dirichlet Multinomial Allocation mixtures. We compare the performance of the Bayesian methods with the classical method through simulation studies. We also make a suggestion on the choice of hyperpriors and hyperparameters.