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 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 Seemingly Unrelated Regression Spatial Autoregressive Bayesian Modeling on Heteroscedasticity Case

2021 ◽  
Vol 2123 (1) ◽  
pp. 012047
Author(s):  
Adiatma
Keyword(s):  
Spatial Data ◽  
Bayesian Modeling ◽  
Autoregressive Model ◽  
Prior Distribution ◽  
Bayesian Method ◽  
Seemingly Unrelated Regression ◽  
Regression Equations ◽  
Spatial Autoregressive Model ◽  
Unrelated Regression ◽  
Spatial Autoregressive

Abstract The phenomenon encountered occasionally on complications involving spatial data, is that there is a tendency of heteroscedasticity since every region has distinct characteristics. Thus, it requires the approach which is more appropriate with the problem by using the Bayesian method. Bayesian method on spatial autoregressive model to contend the heteroscedasticity by applying prior distribution on variance parameter of error. To detect heteroscedasticity, it is shown from several responses correlating with the predictors. The method abled to estimate some responses is Seemingly Unrelated Regression (SUR). SUR is an econometrics model that used to be being utilized in solving some regression equations in which of them has their own parameter and appears to be uncorrelated. However, by correlation of error in differential equations, the correlation would occur among them. With the condition of the Bayesian SUR spatial autoregressive model, it is able to overcome heteroscedasticity cases from the vision of spatial. Further, the model involves four kinds of parameter priors’ distributions estimated by using the process of MCMC.

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.

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