Robust estimation of mean and covariance for longitudinal data with dropouts

In this paper, we study estimation of linear models in the framework of longitudinal data with dropouts. Under the assumptions that random errors follow an elliptical distribution and all the subjects share the same within-subject covariance matrix which does not depend on covariates, we develop a robust method for simultaneous estimation of mean and covariance. The proposed method is robust against outliers, and does not require to model the covariance and missing data process. Theoretical properties of the proposed estimator are established and simulation studies show its good performance. In the end, the proposed method is applied to a real data analysis for illustration.

[1]  Sanjoy K. Sinha,et al.  Robust Analysis of Generalized Linear Mixed Models , 2004 .

[2]  Zhongyi Zhu,et al.  On the asymptotics of marginal regression splines with longitudinal data , 2008 .

[3]  Lin Lu,et al.  Highly Efficient Aggregate Unbiased Estimating Functions Approach for Correlated Data With Missing at Random , 2010 .

[4]  M. Pourahmadi.  Joint mean-covariance models with applications to longitudinal data: Unconstrained parameterisation , 1999 .

[5]  A survey on continuous elliptical vector distributions , 2003 .

[6]  Nicole A. Lazar,et al.  Statistical Analysis With Missing Data , 2003, Technometrics.

[7]  Paul J Rathouz,et al.  Performance of weighted estimating equations for longitudinal binary data with drop‐outs missing at random , 2002, Statistics in medicine.

[8]  Zhongyi Zhu,et al.  Robust estimation in generalized semiparametric mixed models for longitudinal data , 2007 .

[9]  B. Lindsay,et al.  Improving generalised estimating equations using quadratic inference functions , 2000 .

[10]  Wenqing He,et al.  Median Regression Models for Longitudinal Data with Dropouts , 2009, Biometrics.

[11]  Zhong Yi Zhu,et al.  Joint estimation of mean-covariance model for longitudinal data with basis function approximations , 2011, Comput. Stat. Data Anal..

[12]  Regressograms and Mean-Covariance Models for Incomplete Longitudinal Data , 2012 .

[13]  V. Carey,et al.  Working correlation structure misspecification, estimation and covariate design: Implications for generalised estimating equations performance , 2003 .

[14]  Roderick J. A. Little,et al.  Statistical Analysis with Missing Data: Little/Statistical Analysis with Missing Data , 2002 .

[15]  Naisyin Wang.  Marginal nonparametric kernel regression accounting for within‐subject correlation , 2003 .

[16]  Zhongyi Zhu,et al.  Robust Estimation in Generalized Partial Linear Models for Clustered Data , 2005 .

[17]  J. P. Meyer,et al.  Applied Measurement with jMetrik , 2014 .

[18]  Robust estimation of generalized partially linear model for longitudinal data with dropouts , 2016 .

[19]  Chenlei Leng,et al.  Semiparametric Mean–Covariance Regression Analysis for Longitudinal Data , 2009 .

[20]  Xueying Zheng,et al.  Robust estimation in joint mean–covariance regression model for longitudinal data , 2013 .

[21]  M. Pourahmadi.  Maximum likelihood estimation of generalised linear models for multivariate normal covariance matrix , 2000 .

[22]  William E. Griffiths,et al.  Principles of Econometrics , 2008 .

[23]  Z. Bai,et al.  Robust Estimation Using the Huber Function With a Data-Dependent Tuning Constant , 2007 .

[24]  Runze Li,et al.  New local estimation procedure for a non‐parametric regression function for longitudinal data , 2013, Journal of the Royal Statistical Society. Series B, Statistical methodology.

[25]  Guoying Li,et al.  Breakdown properties of location $M$-estimators , 1998 .

[26]  Xiao-Hua Zhou,et al.  Generalized Partially Linear Models for Incomplete Longitudinal Data In the Presence of Population‐Level Information , 2013, Biometrics.

[27]  J. Robins,et al.  Analysis of semiparametric regression models for repeated outcomes in the presence of missing data , 1995 .

[28]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

[29]  Jianxin Pan,et al.  Modelling of covariance structures in generalised estimating equations for longitudinal data , 2006 .