Modeling spatial data using local likelihood estimation and a Matérn to spatial autoregressive translation

2020 ◽  
Vol 31 (6) ◽  
Author(s):  
Ashton Wiens ◽  
Douglas Nychka ◽  
William Kleiber
Keyword(s):  
Spatial Data ◽  
Likelihood Estimation ◽  
Local Likelihood ◽  
Spatial Autoregressive

scholarly journals Functional SAC model: With application to spatial econometrics

2021 ◽  
Vol 55 (1) ◽  
pp. 1-13
Author(s):  
Alassane Aw ◽  
Emmanuel N. Cabral
Keyword(s):  
Maximum Likelihood ◽  
Spatial Econometrics ◽  
Spatial Data ◽  
Estimation Method ◽  
Likelihood Estimation ◽  
Explanatory Variables ◽  
Dependent Variables ◽  
Spatial Autoregressive ◽  
The Relationship ◽  
Maximum Likelihood Estimation Method

Spatial autoregressive combined (SAC) models have been widely studied in the literature for the analysis of spatial data in various areas such as geography, economics, demography, regional sciences. This is a linear model with scalar response and scalar explanatory variables which allows for spatial interactions in the dependent variables and the disturbances. In this work we extend this modeling approach from scalar to functional covariate. The parameters of the model are estimated via the maximum likelihood estimation method. A simulation study is conducted to evaluate the performance of the proposed methodology. As an illustration, the model is used to establish the relationship between unemployment and illiteracy in Senegal.

SPATIAL AUTOREGRESSIVE (SAR) MODEL WITH ENSEMBLE LEARNING-MULTIPLICATIVE NOISE WITH LOGNORMAL DISTRIBUTION (CASE ON POVERTY DATA IN EAST JAVA)

2021 ◽  
Vol 14 (1) ◽  
pp. 89-97
Author(s):  
Dewi Retno Sari Saputro ◽  
Sulistyaningsih Sulistyaningsih ◽  
Purnami Widyaningsih
Keyword(s):  
Regression Model ◽  
Ensemble Learning ◽  
Spatial Data ◽  
Lognormal Distribution ◽  
Multiplicative Noise ◽  
Spatial Regression ◽  
Spatial Error ◽  
Spatial Regression Model ◽  
Sar Model ◽  
Spatial Autoregressive

The regression model that can be used to model spatial data is Spatial Autoregressive (SAR) model. The level of accuracy of the estimated parameters of the SAR model can be improved, especially to provide better results and can reduce the error rate by resampling method. Resampling is done by adding noise (noise) to the data using Ensemble Learning (EL) with multiplicative noise. The research objective is to estimate the parameters of the SAR model using EL with multiplicative noise. In this research was also applied a spatial regression model of the ensemble non-hybrid multiplicative noise which has a lognormal distribution of cases on poverty data in East Java in 2016. The results showed that the estimated value of the non-hybrid spatial ensemble spatial regression model with multiplicative noise with a lognormal distribution was obtained from the average parameter estimation of 10 Spatial Error Model (SEM) resulting from resampling. The multiplicative noise used is generated from lognormal distributions with an average of one and a standard deviation of 0.433. The Root Mean Squared Error (RMSE) value generated by the non-hybrid spatial ensemble regression model with multiplicative noise with a lognormal distribution is 22.99.

Local likelihood estimation of time-variant Hawkes models

2016 ◽  
Author(s):  
Boris I. Godoy ◽  
Victor Solo ◽  
Jason Min ◽  
Syed Ahmed Pasha
Keyword(s):  
Likelihood Estimation ◽  
Local Likelihood ◽  
Estimation Of Time

scholarly journals Bayesian Analysis of Partially Linear Additive Spatial Autoregressive Models with Free-Knot Splines

Symmetry ◽  
2021 ◽  
Vol 13 (9) ◽  
pp. 1635
Author(s):  
Zhiyong Chen ◽  
Jianbao Chen
Keyword(s):  
Spatial Data ◽  
Generalized Method Of Moments ◽  
Bayesian Estimator ◽  
Posterior Distributions ◽  
Computationally Efficient ◽  
Partially Linear ◽  
Spatial Autoregressive ◽  
Method Of Moments Estimator ◽  
Spatial Autoregressive Models ◽  
Convergent Algorithm

This article deals with symmetrical data that can be modelled based on Gaussian distribution. We consider a class of partially linear additive spatial autoregressive (PLASAR) models for spatial data. We develop a Bayesian free-knot splines approach to approximate the nonparametric functions. It can be performed to facilitate efficient Markov chain Monte Carlo (MCMC) tools to design a Gibbs sampler to explore the full conditional posterior distributions and analyze the PLASAR models. In order to acquire a rapidly-convergent algorithm, a modified Bayesian free-knot splines approach incorporated with powerful MCMC techniques is employed. The Bayesian estimator (BE) method is more computationally efficient than the generalized method of moments estimator (GMME) and thus capable of handling large scales of spatial data. The performance of the PLASAR model and methodology is illustrated by a simulation, and the model is used to analyze a Sydney real estate dataset.

scholarly journals Spatial Regression Models: A Systematic Comparison of Different Model Specifications Using Monte Carlo Experiments

2019 ◽  
pp. 004912411988246 ◽  
Author(s):  
Tobias Rüttenauer
Keyword(s):  
Monte Carlo ◽  
Spatial Data ◽  
Regression Models ◽  
Spatial Regression ◽  
Spillover Effects ◽  
Spatial Error ◽  
Monte Carlo Experiments ◽  
Spatial Autoregressive ◽  
Spatial Regression Models ◽  
Variable Bias

Spatial regression models provide the opportunity to analyze spatial data and spatial processes. Yet, several model specifications can be used, all assuming different types of spatial dependence. This study summarizes the most commonly used spatial regression models and offers a comparison of their performance by using Monte Carlo experiments. In contrast to previous simulations, this study evaluates the bias of the impacts rather than the regression coefficients and additionally provides results for situations with a nonspatial omitted variable bias. Results reveal that the most commonly used spatial autoregressive and spatial error specifications yield severe drawbacks. In contrast, spatial Durbin specifications (SDM and SDEM) and the simple spatial lag of X (SLX) provide accurate estimates of direct impacts even in the case of misspecification. Regarding the indirect “spillover” effects, several—quite realistic—situations exist in which the SLX outperforms the more complex SDM and SDEM specifications.

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