Generalized Likelihood Procedures for Data Analysis and Modeling

We present a generalized likelihood (GL) methodology derived from the information generating function. The GL (or GI-based score function in the case of censored or binary data) depends on a user-specified index c, which takes values in a neighborhood of 0. If c = 0, the classical likelihood procedures result. For c > 0, attractive joint robust M-estimators of all model parameters are obtained. Variation of c generates a sensitivity analysis, or informal assessment of consistency of data and assumed model. We apply our framework in univariate and multivariate settings including regression, designed experiments, time series, survival data, parametric proportional hazards models, censored data and binary data. We provide large sample inference results and present formal and informal techniques for model building including order selection, outlier identification, treatment of missing values, and estimation of a transformation power. We examine several examples and special cases