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.
Highlights
Longitudinal data arises frequently in many fields, such as biological research, social science and other fields
We propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters with longitudinal data based on the exponential squared loss (ESL) function
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
Summary
Longitudinal data arises frequently in many fields, such as biological research, social science and other fields. [13] proposed a robust procedure for modeling the correlation matrix of longitudinal data based on an alternative Cholesky decomposition and heavy-tailed multivariate t-distributions with unknown degrees of freedom. M-type regression and quantile regression procedures can overcome outliers and heavy-tail errors, they may lose efficiency under the normal distribution To overcome this difficulty, [20] recently proposed a robust variable selection approach by adopting the exponential squared loss (ESL) function with a tuning parameter. 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 employing the ESL function. We propose a robust estimation approach for the model parameters of the mean and generalized autoregressive parameters in the within subject covariance matrices for longitudinal data based on the ESL function.
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