High-dimensional generalized semiparametric model for longitudinal data

Abstract: This paper considers the problem of estimation in the generalized semiparametric model for longitudinal data when the number of parameters diverges with the sample size. A penalization type of generalized estimating equation method is proposed, while we use the regression spline to approximate the nonparametric component. The proposed procedure involves the specification of the posterior distribution of the random effects, which cannot be evaluated in a closed-form. However, it is possible to approximate this posterior distribution by producing random draws from the distribution using a Metropolis algorithm. Under some regularity conditions, the resulting estimators enjoy the oracle properties, under the high-dimensional regime. Simulation studies are carried out to assess the performance of our proposed method, and two real data sets are analyzed to illustrate the procedure.