Statistics and Its Interface

Volume 15 (2022)

Number 1

Bayesian estimation for partially linear varying coefficient spatial autoregressive models

Pages: 105 – 113

DOI: https://dx.doi.org/10.4310/21-SII682

Authors

Ruiqin Tian (School of Science, Hangzhou Normal University, Hangzhou, China)

Dengke Xu (Department of Statistics, Zhejiang Agriculture and Forestry University, Hangzhou, China)

Jiang Du (School of Statistics and Data Science, Beijing University of Technology, Beijing, China)

Junfei Zhang (School of Statistics and Mathematics, Central University of Finance and Economics, Beijing, China)

Abstract

We propose a fully Bayesian estimation approach for partially linear varying coefficient spatial autoregressive models on the basis of B-spline approximations of nonparametric components. A computational efficient MCMC method that combines the Gibbs sampler with Metropolis–Hastings algorithm is implemented to simultaneously obtain the Bayesian estimates of unknown parameters, as well as their standard error estimates. Monte Carlo simulations are used to investigate the finite sample performance of the proposed method. Finally, a real data analysis of Boston housing data is used to illustrate the usefulness of the proposed methodology.

Keywords

spatial autoregressive models, partially linear varying coefficient models, Bayesian estimate, Gibbs sampler, B-spline

2010 Mathematics Subject Classification

Primary 62F15. Secondary 62G05.

Full Text (PDF format)

Tian’s work was supported by the National Natural Science Foundation of China (11801514), and by the Startup Foundation for Talents at Hangzhou Normal University(2019QDL039).

Xu’s work was supported by the Key Projects of statistical research in Zhejiang Province (20TJZZ13).

Du’s work was supported by the National Natural Science Foundation of China (11971045,11771032), the Natural Science Foundation of Beijing Municipality (1202001), and the Science and Technology Project of Beijing Municipal Education Commission (KM201910005015, KM202010005026).

Received 9 July 2020

Accepted 12 May 2021

Published 11 August 2021