Non-linear regression in credibility theory

Abstract

Let X be a random vector with distribution depending on a parameter treated as a random variable ⊝. The usual linear regression assumption is that E( X|⊝) can be displayed in the form yβ(⊝) where y is a fixed design matrix and β(⊝) an unknown vector. In the present paper we assume that E( X|⊝) is a rather arbitrary function ƒ(β(⊝)) of the unknown vector β(⊝) and we derive credibility approximations for β(⊝).