ESL-Based Robust Estimation for Mean-Covariance Regression with Longitudinal Data
Open Access
- 1 January 2020
- journal article
- Published by Scientific Research Publishing, Inc. in Open Journal of Statistics
- Vol. 10 (01), 10-30
- https://doi.org/10.4236/ojs.2020.101002
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.Keywords
This publication has 28 references indexed in Scilit:
- Variable selection in robust joint mean and covariance model for longitudinal data analysisStatistica Sinica, 2014
- A moving average Cholesky factor model in covariance modelling for longitudinal dataBiometrika, 2011
- Robust StatisticsPublished by Springer Science and Business Media LLC ,2011
- Modeling covariance matrices via partial autocorrelationsJournal of Multivariate Analysis, 2009
- Cholesky Decompositions and Estimation of A Covariance Matrix: Orthogonality of Variance Correlation ParametersBiometrika, 2007
- Modelling of covariance structures in generalised estimating equations for longitudinal dataBiometrika, 2006
- On modelling mean-covariance structures in longitudinal studiesBiometrika, 2003
- Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrixBiometrika, 2000
- Joint mean-covariance models with applications to longitudinal data: unconstrained parameterisationBiometrika, 1999
- Longitudinal data analysis using generalized linear modelsBiometrika, 1986