Robust Inference Progress from Independent to Longitudinal Setup

Abstract

In practice one may not have always smooth data. When bulk of the data are smooth but the complete data set apparently contains a few contaminated observations or outliers, one encounters difficulties to choose an inference technique because of the fact that the traditional inference techniques developed for smooth data analysis may no longer provide unbiased and consistent estimates for the desired parameters such as regression parameters in linear or generalized linear models (GLMs) setup. In this paper, we first briefly review some of the widely used bias corrected techniques in linear model setup. But, as opposed to the linear models in normal or other continuous exponential family based variables, the robust inference for discrete data in the GLMs setup, such as for count and binary data, is, however, not adequately discussed in the literature. The advantages and drawbacks of an existing outliers resistant Mallow’s type quasi-likelihood (MQL) estimation approach in GLMs setup are reviewed in brief. We then discuss a recently proposed fully standardized MQL (FSMQL) approach that provides almost unbiased estimates ensuring its higher consistency performance. One encounters further challenges when the data in GLMs setup are repeatedly collected over a period of time. This is mainly because one then requires to modify the FSMQL type estimation approaches such that the modified approach also accommodates the correlation structure of the repeated data. A recently proposed robust generalized QL (RGQL) approach is reviewed for the purpose.