Open AccessSimultaneous variable selection and estimation for longitudinal ordinal data with a diverging number of covariates
Author(s) -
Xianbin Chen,
AUTHOR_ID,
Juliang Yin
Publication year - 2022
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022402
Subject(s) - mathematics , covariate , estimator , multinomial distribution , statistics , dimension (graph theory) , ordinal data , variable (mathematics) , combinatorics , mathematical analysis
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.