Functional varying-coefficient model under heteroskedasticity with application to DTI data

TL;DR

This paper introduces a novel multi-step estimation method for varying-coefficient models that accounts for heteroskedasticity and spatial dependence, improving estimation accuracy with theoretical and empirical validation.

Contribution

It develops a local-linear GMM approach with an optimal instrument for better estimation under heteroskedasticity and spatial dependence, addressing key challenges in functional data analysis.

Findings

Enhanced estimation accuracy demonstrated through simulations

Optimal instrument reduces asymptotic variance

Real data analysis confirms method's effectiveness

Abstract

In this paper, we develop a multi-step estimation procedure to simultaneously estimate the varying-coefficient functions using a local-linear generalized method of moments (GMM) based on continuous moment conditions. To incorporate spatial dependence, the continuous moment conditions are first projected onto eigen-functions and then combined by weighted eigen-values, thereby, solving the challenges of using an inverse covariance operator directly. We propose an optimal instrument variable that minimizes the asymptotic variance function among the class of all local-linear GMM estimators, and it outperforms the initial estimates which do not incorporate the spatial dependence. Our proposed method significantly improves the accuracy of the estimation under heteroskedasticity and its asymptotic properties have been investigated. Extensive simulation studies illustrate the finite sample performance, and the efficacy of the proposed method is confirmed by real data analysis.