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Lv, J. and Guo, C. (2019) Quantile Estimations via Modified Cholesky Decomposition for Longitudinal Single-Index Models. Annals of the Institute of Statistical Mathematics, 71, 1163-1199.
https://doi.org/10.1007/s10463-018-0673-x

has been cited by the following article:

  • TITLE: ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data

    AUTHORS: Fei Lu, Liugen Xue, Xiong Cai

    KEYWORDS: Exponential Squared Loss Function, Within-Subject Correlation, Longitudinal Data, Modified Cholesky Decomposition, Robustness

    JOURNAL NAME: Open Journal of Statistics, Vol.10 No.1, January 13, 2020

    ABSTRACT: When longitudinal data contains outliers, the classical least-squares approach is known to be not robust. To solve this issue, the exponential squared loss (ESL) function with a tuning parameter has been investigated for longitudinal data. However, to our knowledge, there is no paper to investigate the robust estimation procedure against outliers within the framework of mean-covariance regression analysis for longitudinal data using the ESL function. In this paper, we propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the ESL function. The proposed estimators can be shown to be asymptotically normal under certain conditions. Moreover, we develop an iteratively reweighted least squares (IRLS) algorithm to calculate the parameter estimates, and the balance between the robustness and efficiency can be achieved by choosing appropriate data adaptive tuning parameters. Simulation studies and real data analysis are carried out to illustrate the finite sample performance of the proposed approach.