Robust empirical likelihood inference for generalized partial linear models with longitudinal data

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: AMS 2000 subject classification: 46N30 Keywords: B-spline Efficiency Empirical likelihood Generalized estimating equations Generalized partial linear models Longitudinal data Robustness a b s t r a c t In this paper, we propose a robust empirical likelihood (REL) inference for the parametric component in a generalized partial linear model (GPLM) with longitudinal data. We make use of bounded scores and leverage-based weights in the auxiliary random vectors to achieve robustness against outliers in both the response and covariates. Simulation studies demonstrate the good performance of our proposed REL method, which is more accurate and efficient than the robust generalized estimating equation (GEE) method (The proposed robust method is also illustrated by analyzing a real data set. Generalized partial linear models (GPLMs) can be regarded as an integration of generalized linear models (GLMs) [10] and fully nonparametric models. By involving both parametric and nonparametric components, GPLMs have great flexibility in modeling real data, and therefore have attracted many research interests and are widely used in practice. The inference for GPLMs is usually based on maximum likelihood method and generalized estimating equation (GEE) method [8]. However, both the classical maximum likelihood and GEE methods are sensitive to outliers. In longitudinal studies, an outlier in a subject-level measurement can result in multiple outliers in the sample. So many robust methods have been developed to limit the impact of the outliers, e.g., [14,3,2,23]. Particularly, for the GPLMs with longitudinal data, He et al. [4] proposed a robust GEE (RGEE) method by using B-spline to approximate the nonparametric function. The commonly used sandwich method was adopted to obtain the variance estimation of their proposed RGEE estimator for the parametric component. However, it is well known that the sandwich method usually underestimates the variance of the GEE estimator, which possibly leads to biased statistical inference. For more detail and systematic introductions about the robust statistical methods we can refer to the book of Heritier et al. [6]. The empirical likelihood (EL) method, first developed by Owen [11], is a popular statistical inference method and has attracted a great deal of interests [7,16]. Many advantages of the EL over the normal approximation-based method have been shown in …