Generalized linear and additive models with weighted distribution

Abstract

In many practical problems, due to constraints on ascertainment, the chances of individuals being sampled from the population differ from individual to individual, which cause what is referred to as the sampling bias. Ignoring the sampling bias in statistical inference can cause serious problems and result in misleading conclusions. This gives rise to the notion of weighted distribution.In this thesis, we study generalized linear and additive models with weighted response variables that include linear regression models as special cases. A systematic treatment is made to the generalized linear and additive models with weighted exponential families. The general theory on the formulation of these models and their properties are established. Various aspects of these models such as the estimation, diagnostics and inference are studied. Computation algorithms are developed. A comprehensive simulation study is carried out to evaluate the effect of sampling bias on the generalized linear and additive models as well.