Abstract

In this paper, we develop a multi-step estimation procedure to simulta

neously 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.

Information

Preprint No.SS-2023-0366
Manuscript IDSS-2023-0366
Complete AuthorsPratim Guha Niyogi, Ping-Shou Zhong, Xiaohong Joe Zhou
Corresponding AuthorsPratim Guha Niyogi
Emailspgniyogi@gmail.com

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Acknowledgments

The research was partially supported by an NIH grant R03NS128450 and an

NSF grant FRG-2152070. The authors thank Editor Prof. John Stufken,

the Associate Editor, and the two referees for their constructive comments,

which significantly improved the paper.

Supplementary Materials

The online supplementary material contains the proposed algorithm, the extension of the proposed method for the multivariate functional domain, com-

ments on assumptions, additional simulation results, proofs of the theorems

presented in Section 4, and a discussion on the choice of IVs.

Supplementary materials are available for download.