Statistical inference in functional semiparametric spatial autoregressive model

Gaosheng Liu; Yang Bai; Gaosheng Liu; Yang Bai

doi:10.3934/math.2021633

AIMS Mathematics

2021, Volume 6, Issue 10: 10890-10906. doi: 10.3934/math.2021633

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Research article

Statistical inference in functional semiparametric spatial autoregressive model

Gaosheng Liu ^{1
,
,},
Yang Bai ²

1.
School of Sciences, Tianjin University of Commerce, Tianjin, 300134, China
2.
School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai 200433, China

Received: 26 January 2021 Accepted: 15 July 2021 Published: 28 July 2021
MSC : 62G05, 62J05, 62M30

Semiparametric spatial autoregressive model has drawn great attention since it allows mutual dependence in spatial form and nonlinear effects of covariates. However, with development of scientific technology, there exist functional covariates with high dimensions and frequencies containing rich information. Based on high-dimensional covariates, we propose an interesting and novel functional semiparametric spatial autoregressive model. We use B-spline basis function to approximate the slope function and nonparametric function and propose generalized method of moments to estimate parameters. Under certain regularity conditions, the asymptotic properties of the proposed estimators are obtained. The estimators are computationally convenient with closed-form expression. For slope function and nonparametric function estimators, we propose the residual-based approach to derive its pointwise confidence interval. Simulation studies show that the proposed method performs well.
- semiparametric spatial autoregressive model,
- functional data analysis,
- B-spline approximation,
- generalized method of moments
Citation: Gaosheng Liu, Yang Bai. Statistical inference in functional semiparametric spatial autoregressive model[J]. AIMS Mathematics, 2021, 6(10): 10890-10906. doi: 10.3934/math.2021633

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Abstract

Semiparametric spatial autoregressive model has drawn great attention since it allows mutual dependence in spatial form and nonlinear effects of covariates. However, with development of scientific technology, there exist functional covariates with high dimensions and frequencies containing rich information. Based on high-dimensional covariates, we propose an interesting and novel functional semiparametric spatial autoregressive model. We use B-spline basis function to approximate the slope function and nonparametric function and propose generalized method of moments to estimate parameters. Under certain regularity conditions, the asymptotic properties of the proposed estimators are obtained. The estimators are computationally convenient with closed-form expression. For slope function and nonparametric function estimators, we propose the residual-based approach to derive its pointwise confidence interval. Simulation studies show that the proposed method performs well.

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