Empirical process based on the recursive residuals in functional measurement error models

Abstract

Recursive residuals are a linear transformation of ordinary residuals. They have frequently been suggested for testing model fit and model assumptions in linear regression. In this paper, we generalize the theory of the empirical process based on the residuals in the measurement error models to the recursive residuals in the measurement error models. We prove that recursive residuals in these models are asymptotically independent and identically distributed and show that, in this case, the weak convergence properties of the standardized residuals hold for the studentized recursive residuals. Furthermore, we look at some tests for goodness-of-fit based on the weak convergence of the empirical distribution of the recursive residuals. We justify the use of goodness-of-fit tests based on recursive residuals by carrying out a parametric bootstrap simulation study.