Robust variable selection with exponential squared loss for the spatial autoregressive model

Song, Yong; Liang, Xijun; Zhu, Yanji; Lin, Lu

doi:10.1016/j.csda.2020.107094

Cited by 18 publications

(10 citation statements)

References 23 publications

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“…The asymptotic distribution of ρn has the √ n/d n -rate of convergence in Theorem 5. As d n is divergent, this rate of convergence is lower than √ n. The asymptotic distribution of the QML estimator βn and its low rate of convergence in Theorem 6 are determined by the asymptotic distribution of ρn that forms the leading term in the asymptotic expansion (29). When β 0 = 0, this leading term vanishes and βn converges to β 0 with the usual √ n-rate.…”

Section: Proof See Appendix Amentioning

confidence: 98%

“…Liu et al [21] developed a penalized quasimaximum likelihood method for simultaneous model selection and parameter estimation in the SAR models with independent and identical distributed errors. Song et al [29] proposed a variable selection method based on exponential squared loss for the SAR models. Ju et al [30] developed Bayesian influence analysis for skew-normal spatial autoregression models (SSARMs).…”

Section: Introductionmentioning

confidence: 99%

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Asymptotic Properties of Quasi-Maximum Likelihood Estimators for Heterogeneous Spatial Autoregressive Models

Qiu¹,

Ding

2022

Symmetry

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In this paper, we address a class of heterogeneous spatial autoregressive models with all n(n−1) spatial coefficients taking m distinct true values, where m is independent of the sample size n, and we establish asymptotic properties of the maximum likelihood estimator and the quasi-maximum likelihood estimator for all parameters in the class of models, extending Lee’s work (2004). The rates of convergence of those estimators depend on the features of values taken by elements of the spatial weights matrix in this model. Under the situations where, based on the values of the weights, each individual will not only influence a few neighbors but also be influenced by only a few neighbors, the estimator can enjoy an n-rate of convergence and be asymptotically normal. However, when each individual can influence many neighbors or can be influenced by many neighbors and their number does not exceed o(n), singularity of the information matrix may occur, and various components of the estimators may have different (usually lower than n) rates of convergence. An inconsistent estimator is provided if some important assumptions are violated. Finally, simulation studies demonstrate that the finite sample performances of maximum likelihood estimators are good.

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Section: Proof See Appendix Amentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Asymptotic Properties of Quasi-Maximum Likelihood Estimators for Heterogeneous Spatial Autoregressive Models

Qiu¹,

Ding

2022

Symmetry

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show abstract

“…Various robust losses have been proposed to deal with the problem instead of least squares loss. The commonly used robust losses mainly include adaptive Huber loss [11], gain function [12], minimum error entropy [13], exponential squared loss [14], etc. Among them, the Maximum Correntropy Criterion (MCC) is widely employed as an efficient alternative to the ordinary least squares method which is suboptimal in the non-Gaussian and non-linear signal processing situations [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Maximum Correntropy Criterion with Distributed Method

Xie

Wang

et al. 2022

Mathematics

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The Maximum Correntropy Criterion (MCC) has recently triggered enormous research activities in engineering and machine learning communities since it is robust when faced with heavy-tailed noise or outliers in practice. This work is interested in distributed MCC algorithms, based on a divide-and-conquer strategy, which can deal with big data efficiently. By establishing minmax optimal error bounds, our results show that the averaging output function of this distributed algorithm can achieve comparable convergence rates to the algorithm processing the total data in one single machine.

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“…Liu et al (2021) [ 20 ] studied variable selection for the spatial autoregressive model with autoregressive disturbances. Song et al (2021) [ 21 ] proposed a new robust variable selection method with an exponential squared loss for the spatial autoregressive model.…”

Section: Introductionmentioning

confidence: 99%

Variable Selection of Spatial Logistic Autoregressive Model with Linear Constraints

Song

Wang

2022

Entropy

Self Cite

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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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Robust variable selection with exponential squared loss for the spatial autoregressive model

Cited by 18 publications

References 23 publications

Asymptotic Properties of Quasi-Maximum Likelihood Estimators for Heterogeneous Spatial Autoregressive Models

Asymptotic Properties of Quasi-Maximum Likelihood Estimators for Heterogeneous Spatial Autoregressive Models

Maximum Correntropy Criterion with Distributed Method

Variable Selection of Spatial Logistic Autoregressive Model with Linear Constraints

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