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AIMS Mathematics

2022, Volume 7, Issue 4: 7199-7211. doi: 10.3934/math.2022402
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Research article

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

  • School of Economics and Statistics, Guangzhou University, Guangzhou, 510006, China
  • Received: 01 November 2021 Revised: 18 January 2022 Accepted: 26 January 2022 Published: 09 February 2022

  • MSC : 62E20, 62F12, 62J12

  • 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.

    Citation: Xianbin Chen, Juliang Yin. Simultaneous variable selection and estimation for longitudinal ordinal data with a diverging number of covariates[J]. AIMS Mathematics, 2022, 7(4): 7199-7211. doi: 10.3934/math.2022402

    Related Papers:

  • 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.


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