The Annals of Statistics

A semiparametric spatial dynamic model

Yan Sun, Hongjia Yan, Wenyang Zhang, and Zudi Lu

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Stimulated by the Boston house price data, in this paper, we propose a semiparametric spatial dynamic model, which extends the ordinary spatial autoregressive models to accommodate the effects of some covariates associated with the house price. A profile likelihood based estimation procedure is proposed. The asymptotic normality of the proposed estimators are derived. We also investigate how to identify the parametric/nonparametric components in the proposed semiparametric model. We show how many unknown parameters an unknown bivariate function amounts to, and propose an AIC/BIC of nonparametric version for model selection. Simulation studies are conducted to examine the performance of the proposed methods. The simulation results show our methods work very well. We finally apply the proposed methods to analyze the Boston house price data, which leads to some interesting findings.

Article information

Ann. Statist., Volume 42, Number 2 (2014), 700-727.

First available in Project Euclid: 20 May 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G08: Nonparametric regression
Secondary: 62G05: Estimation 62G20: Asymptotic properties

AIC/BIC local linear modeling profile likelihood spatial interaction


Sun, Yan; Yan, Hongjia; Zhang, Wenyang; Lu, Zudi. A semiparametric spatial dynamic model. Ann. Statist. 42 (2014), no. 2, 700--727. doi:10.1214/13-AOS1201.

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