A Unified Approach to Regression Analysis under Double Sampling Design

Abstract

We generalise Hampel's influence function (1968, 1974) to the second order partial derivative of a statistical functional. This generalisation of Hampel's influence function is closely related to the second order differentiation approach in linear models. Based on the second order derivative, a specific type of influence related to the masking effect of one observation by another observation is drawn. This type of influence is referred to as the ?€?interaction influence?€?. Different types of influence can be described in terms of set theory. The generalization of Hampel's influence function and the second order differentiation approach has the potential of unmasking the masked observations. In addition, a local influence method related to both the proposed generalization of Hampel's influence function and the proposed differentiation approach is developed. The method is not restricted to linear regression models. Several illustrative examples based on real data are presented. This paper is a joint work with Dr. Kosorok.