Simultaneous variable selection and estimation for longitudinal ordinal data with a diverging number of covariates

In this paper, we study the problem of simultaneous variable selection and estimation for longitudinal ordinal data with high-dimensional covariates. Using the penalized generalized estimation equation (GEE) method, we obtain some asymptotic properties for these types of data in the case that the dimension of the covariates p(n) tends to infinity as the number of cluster n approaches to infinity. More precisely, under appropriate regular conditions, all the covariates with zero coefficients can be examined simultaneously with probability tending to 1, and the estimator of the non-zero coefficients exhibits the asymptotic Oracle properties. Finally, we also perform some Monte Carlo studies to illustrate the theoretical analysis. The main result in this paper extends the elegant work of Wang et al. [1] to the multinomial response variable case.

Automated summary

This paper studies the problem of simultaneous variable selection and estimation for longitudinal ordinal data with high-dimensional covariates. The penalized generalized estimation equation (GEE) method is used to obtain asymptotic properties for these data. The main result shows that under appropriate conditions, all covariates with zero coefficients can be examined simultaneously, and the estimator of non-zero coefficients exhibits asymptotic Oracle properties. Monte Carlo studies are conducted to demonstrate the theoretical analysis.