Statistics and Its Interface

Volume 17 (2024)

Number 3

Estimation of partially linear varying coefficient spatial autoregressive models

Pages: 371 – 382

DOI: https://dx.doi.org/10.4310/23-SII775

Authors

Xiaoying Wang (North China Electric Power University, Beijing)

Xiaoqian Sun (Beijing University of Technology)

Jiang Du (Beijing University of Technology)

Kaiyuan Liu (Beijing University of Technology)

Abstract

Partially linear varying coefficient spatial autoregressive (PLVCSAR) models are powerful tools for analyzing data with complex features such as non-linearity, interactions between predictors, and spatial dependence. This paper studies the estimation of the PLVCSAR model by combining the profile quasi-maximum likelihood method and the spline approximation technique. Estimations of the constant coefficients, function coefficients, variance of the error term, and the spatial lag parameter are proposed. Under mild conditions, the asymptotic properties of the proposed estimators are established. Simulation studies and real data analysis of Boston housing data illustrate the finite sample performances of the proposed estimators.

Keywords

spatial dependence, polynomial splines, profile maximum likelihood, asymptotic properties

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Received 15 October 2022

Accepted 11 January 2023

Published 19 July 2024