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.