Regression analysis under non-standard situations: a pairwise pseudolikelihood approach

Regression analysis is one of the most used statistical methods for data an alysis. There are, however, many situations in which one cannot base infere nce solely on f(y \ x; beta), the conditional probability (density) functio n for the response variable Y, given x, the covariates. Examples include mi ssing data where the missingness is non-ignorable, sampling surveys in whic h subjects are selected on the basis of the Y-values and meta-analysis wher e published studies are subject to 'selection bias'. The conventional appro aches require the correct specification of the missingness mechanism, sampl ing probability and probability for being published respectively. In this p aper, we propose an alternative estimating procedure for beta based on an i dea originated by Kalbfleisch. The novelty of this method is that no assump tion on the missingness probability mechanisms etc. mentioned above is requ ired to be specified. Asymptotic efficiency calculations and simulation stu dies were conducted to compare the method proposed with the two existing me thods: the conditional likelihood and the weighted estimating function appr oaches.