Influence measures on corrected score estimators in functional heteroscedastic measurement error models

Abstract

This paper deals with the local influence assessment of the effects of minor perturbations of data on corrected score estimators in the functional heteroscedastic measurement error models with known variances. By extending to the context of measurement error models the differential-geometrical framework proposed by Zhu et al. [H.T. Zhu, J.G. Ibrahim, S. Lee, H. Zhang, Perturbation selection and influence measures in local influence analysis, The Annals of Statistics 35 (2007) 2565–2588], an n-dimensional Riemannian manifold is defined. The associated metric tensor is utilized for the selection of appropriate perturbation schemes. The Levi-Civita connection and first and second derivatives of the corrected score estimators are used to construct influence measures. Simple formulas are obtained under different perturbation schemes. A comparison with the slope and curvature based diagnostics defined from the surface of the corrected score estimators formed by perturbation is included. A real data application and a simulated example illustrate the performance of the proposed diagnostics.