SENSITIVITY ANALYSIS IN FUNCTIONAL REGRESSION MODELS FOR SCALAR RESPONSES

Abstract

In this paper, we propose a method of sensitivity analysis in functional regression models for scalar responses. We define a Cook's D type distance in functional regression analysis (FRA) based on two kinds of influence functions: 1) Empirical Influence Function (EIF), 2) Sample Influence function (SIF). In ordinary regression analysis (ORA), the Cook's D distance can be expressed as a function of residual and leverage. We define diagnostic statistics which correspond to residual and leverage in ORA, and show our Cook's D type distances in FRA are functions of these diagnostic statistics. We give a numerical example to show the properties of two types of Cook's D type distance and these diagnostic statistics.