scholarly journals Statistical inference in functional semiparametric spatial autoregressive model

2021 ◽  
Vol 6 (10) ◽  
pp. 10890-10906
Author(s):  
Gaosheng Liu ◽  
◽  
Yang Bai ◽  
Keyword(s):  
Autoregressive Model ◽  
Asymptotic Properties ◽  
Generalized Method Of Moments ◽  
Nonlinear Effects ◽  
Closed Form Expression ◽  
Regularity Conditions ◽  
Spatial Autoregressive Model ◽  
Nonparametric Function ◽  
Spatial Autoregressive ◽  
Slope Function

<abstract><p>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.</p></abstract>

scholarly journals Estimation in Partial Functional Linear Spatial Autoregressive Model

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1680
Author(s):  
Yuping Hu ◽  
Siyu Wu ◽  
Sanying Feng ◽  
Junliang Jin
Keyword(s):  
Autoregressive Model ◽  
Estimation Method ◽  
Random Variable ◽  
Regularity Conditions ◽  
Functional Regression ◽  
Finite Sample ◽  
Spatial Autoregressive Model ◽  
Explanatory Variables ◽  
Spatial Autoregressive ◽  
Slope Function

Functional regression allows for a scalar response to be dependent on a functional predictor; however, not much work has been done when response variables are dependence spatial variables. In this paper, we introduce a new partial functional linear spatial autoregressive model which explores the relationship between a scalar dependence spatial response variable and explanatory variables containing both multiple real-valued scalar variables and a function-valued random variable. By means of functional principal components analysis and the instrumental variable estimation method, we obtain the estimators of the parametric component and slope function of the model. Under some regularity conditions, we establish the asymptotic normality for the parametric component and the convergence rate for slope function. At last, we illustrate the finite sample performance of our proposed methods with some simulation studies.

scholarly journals Bayesian Estimation of Partially Linear Additive Spatial Autoregressive Models with P-Splines

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Zhiyong Chen ◽  
Minghui Chen ◽  
Guodong Xing
Keyword(s):  
Spatial Data ◽  
Autoregressive Model ◽  
Estimation Method ◽  
Additive Model ◽  
Housing Price ◽  
Nonlinear Effects ◽  
Spatial Autoregressive Model ◽  
Unknown Parameters ◽  
Partially Linear ◽  
Spatial Autoregressive

In this paper, we aim to develop a partially linear additive spatial autoregressive model (PLASARM), which is a generalization of the partially linear additive model and spatial autoregressive model. It can be used to simultaneously evaluate the linear and nonlinear effects of the covariates on the response for spatial data. To estimate the unknown parameters and approximate nonparametric functions by Bayesian P-splines, we develop a Bayesian Markov Chain Monte Carlo approach to estimate the PLASARM and design a Gibbs sampler to explore the joint posterior distributions of unknown parameters. Furthermore, we illustrate the performance of the proposed model and estimation method by a simulation study and analysis of Chinese housing price data.

scholarly journals Variable Selection for the Spatial Autoregressive Model with Autoregressive Disturbances

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1448
Author(s):  
Xuan Liu ◽  
Jianbao Chen
Keyword(s):  
Variable Selection ◽  
Autoregressive Model ◽  
Rapid Development ◽  
Heterogeneous Data ◽  
Spatial Effect ◽  
Spatial Effects ◽  
Spatial Autoregressive Model ◽  
Monte Carlo Studies ◽  
Spatial Autoregressive ◽  
Theoretical Results

Along with the rapid development of the geographic information system, high-dimensional spatial heterogeneous data has emerged bringing theoretical and computational challenges to statistical modeling and analysis. As a result, effective dimensionality reduction and spatial effect recognition has become very important. This paper focuses on variable selection in the spatial autoregressive model with autoregressive disturbances (SARAR) which contains a more comprehensive spatial effect. The variable selection procedure is presented by using the so-called penalized quasi-likelihood approach. Under suitable regular conditions, we obtain the rate of convergence and the asymptotic normality of the estimators. The theoretical results ensure that the proposed method can effectively identify spatial effects of dependent variables, find spatial heterogeneity in error terms, reduce the dimension, and estimate unknown parameters simultaneously. Based on step-by-step transformation, a feasible iterative algorithm is developed to realize spatial effect identification, variable selection, and parameter estimation. In the setting of finite samples, Monte Carlo studies and real data analysis demonstrate that the proposed penalized method performs well and is consistent with the theoretical results.

scholarly journals Estimation of Partially Specified Spatial Autoregressive Model

2014 ◽  
Vol 2 (3) ◽  
pp. 226-235
Author(s):  
Yuanqing Zhang
Keyword(s):  
Autoregressive Model ◽  
Instrumental Variable ◽  
Error Term ◽  
Sufficient Conditions ◽  
Spatial Autoregressive Model ◽  
Dimensional Parameter ◽  
Instrumental Variable Estimation ◽  
Weighting Matrix ◽  
Finite Dimensional ◽  
Spatial Autoregressive

Abstract In this paper, we study estimation of a partially specified spatial autoregressive model with heteroskedasticity error term. Under the assumption of exogenous regressors and exogenous spatial weighting matrix, we propose an instrumental variable estimation. Under some sufficient conditions, we show that the proposed estimator for the finite dimensional parameter is root-n consistent and asymptotically normally distributed and the proposed estimator for the unknown function is consistent and also asymptotically distributed though at a rate slower than root-n. Monte Carlo simulations verify our theory and the results suggest that the proposed method has some practical value.

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