Robust Inference for Time-Varying Coefficient Models with Longitudinal Data  

作　　者：Zhaofeng Wang Jiancheng Jiang Qunyi Qiu 

机构地区：[1]Jishou University, Jishou, China [2]University of North Carolina, Charlotte, NC, USA [3]Peking University, Bejing, China

出　　处：《Open Journal of Statistics》2015年第7期702-713,共12页统计学期刊（英文）

摘　　要：Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for estimating the coefficient functions and develop a robustified generalized likelihood ratio (GLR) statistic to test if some of the coefficient functions are constants or of certain parametric forms. The robustified GLR test is robust against outliers and the error distribution. This provides a useful robust inference tool for the models with longitudinal data. The bandwidth selection issue is also addressed to facilitate the implementation in practice. Simulations show that the proposed testing method is more powerful in some situations than its counterpart based on the least squares principle. A real example is also given for illustration.Time-varying coefficient models are useful in longitudinal data analysis. Various efforts have been invested for the estimation of the coefficient functions, based on the least squares principle. Related work includes smoothing spline and kernel methods among others, but these methods suffer from the shortcoming of non-robustness. In this paper, we introduce a local M-estimation method for estimating the coefficient functions and develop a robustified generalized likelihood ratio (GLR) statistic to test if some of the coefficient functions are constants or of certain parametric forms. The robustified GLR test is robust against outliers and the error distribution. This provides a useful robust inference tool for the models with longitudinal data. The bandwidth selection issue is also addressed to facilitate the implementation in practice. Simulations show that the proposed testing method is more powerful in some situations than its counterpart based on the least squares principle. A real example is also given for illustration.

关 键 词：LOCAL POLYNOMIAL SMOOTHING Longitudinal Data LOCAL M-ESTIMATORS Generalized LIKELIHOOD RATIO Tests 

分 类 号：R73[医药卫生—肿瘤]