A penalized quasi-maximum likelihood method for variable selection in the spatial autoregressive model

Li, Xuan; Chen, Jianbao; Cheng, Suli

doi:10.1016/j.spasta.2018.05.001

Cited by 47 publications

(11 citation statements)

References 29 publications

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“…We compare the following approaches: the conventional quantile regression method with instrument variables (RQ), the Fused LASSO method without adaptive weights (FL), the Fused Adaptive LASSO (FAL) method, the Fused Sup-norm method without adaptive weights (FS), and the Fused Adaptive Sup-norm (FAS) method. To evaluate various approaches, we examine the median of squared error (MedSE), that is the median of θ(k) − θ (k) 2 over 500 simulations, which has been used in Liu et. al.…”

Section: Simulation Studymentioning

confidence: 99%

Interquantile Shrinkage in Spatial Quantile Autoregressive Regression models

Dong¹,

Hou²,

Song³

2021

Preprint

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Spatial dependent data frequently occur in many fields such as spatial econometrics and epidemiology. To deal with the dependence of variables and estimate quantile-specific effects by covariates, spatial quantile autoregressive models (SQAR models) are introduced. Conventional quantile regression only focuses on the fitting models but ignores the examination of multiple conditional quantile functions, which provides a comprehensive view of the relationship between the response and covariates. Thus, it is necessary to study the different regression slopes at different quantiles, especially in situations where the quantile coefficients share some common feature. However, traditional Wald multiple tests not only increase the burden of computation but also bring greater FDR. In this paper, we transform the estimation and examination problem into a penalization problem, which estimates the parameters at different quantiles and identifies the interquantile commonality at the same time. To avoid the endogeneity caused by the spatial lag variables in SQAR models, we also introduce instrumental variables before estimation and propose two-stage estimation methods based on fused adaptive LASSO and fused adaptive sup-norm penalty approaches. The oracle properties of the proposed estimation methods are established. Through numerical investigations, it is demonstrated that the

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Section: Simulation Studymentioning

confidence: 99%

Interquantile Shrinkage in Spatial Quantile Autoregressive Regression models

Dong¹,

Hou²,

Song³

2021

Preprint

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“…To the best of our knowledge, Liu et al [18] investigated variable selection in the SAR model with independent and identically distributed errors, but their model was not under the situation of a diverging number of parameters and the asymptotic properties they established were not available for high-dimensional data. Xie et al [19] considered the penalized estimation for SAR models with a diverging number of parameters and established the oracle properties; however, their method was available for high-dimensional crosssectional data but not for panel data.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection of High-Dimensional Spatial Autoregressive Panel Models with Fixed Effects

Xia

Zhang

Tian

2023

Journal of Mathematics

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This paper studies the variable selection of high-dimensional spatial autoregressive panel models with fixed effects in which a matrix transformation method is applied to eliminate the fixed effects. Then, a penalized quasi-maximum likelihood is developed for variable selection and parameter estimation in the transformed panel model. Under some regular conditions, the consistency and oracle properties of the proposed estimator are established. Some Monte-Carlo experiments and a real data analysis are conducted to examine the finite sample performance of the proposed variable selection procedure, showing that the proposed variable selection method works satisfactorily.

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“…For example, Piribauer et al (2016) [ 13 ] proposed a Bayesian variable selection procedure in a spatial autoregressive model. A penalized quasi-maximum likelihood method was put forth by Liu et al (2018) [ 14 ] for variable selection in the spatial autoregressive model. Model selection in spatial autoregressive models with varying coefficients was studied by Wei et al (2019) [ 15 ].…”

Section: Introductionmentioning

confidence: 99%

Variable Selection of Spatial Logistic Autoregressive Model with Linear Constraints

Song

Wang

2022

Entropy

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In recent years, spatial data widely exist in various fields such as finance, geology, environment, and natural science. These data collected by many scholars often have geographical characteristics. The spatial autoregressive model is a general method to describe the spatial correlations among observation units in spatial econometrics. The spatial logistic autoregressive model augments the conventional logistic regression model with an extra network structure when the spatial response variables are discrete, which enhances classification precision. In many application fields, prior knowledge can be formulated as constraints on the parameters to improve the effectiveness of variable selection and estimation. This paper proposes a variable selection method with linear constraints for the high-dimensional spatial logistic autoregressive model in order to integrate the prior information into the model selection. Monte Carlo experiments are provided to analyze the performance of our proposed method under finite samples. The results show that the method can effectively screen out insignificant variables and give the corresponding coefficient estimates of significant variables simultaneously. As an empirical illustration, we apply our method to land area data.

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A penalized quasi-maximum likelihood method for variable selection in the spatial autoregressive model

Cited by 47 publications

References 29 publications

Interquantile Shrinkage in Spatial Quantile Autoregressive Regression models

Interquantile Shrinkage in Spatial Quantile Autoregressive Regression models

Variable Selection of High-Dimensional Spatial Autoregressive Panel Models with Fixed Effects

Variable Selection of Spatial Logistic Autoregressive Model with Linear Constraints

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