期刊
COMPUTATIONAL STATISTICS & DATA ANALYSIS
卷 155, 期 -, 页码 -出版社
ELSEVIER
DOI: 10.1016/j.csda.2020.107094
关键词
Spatial autoregressive model; Exponential squared loss; Oracle property; Adaptive lasso; Variable selection
资金
- NNSF of China [11971265]
- Natural Science Foundation(NSF) project of Shandong Province of China [ZR2019MA016]
- Fundamental Research Funds for the Central Universities [20CX05012A]
This study proposes a robust regression estimator based on penalized exponential squared loss for general spatial autoregressive models. The method employs an adaptive lasso penalty for simultaneous model selection and parameter estimation. Numerical studies show that the proposed method is particularly robust when dealing with outliers or intensive noise.
Spatial dependent data frequently occur in spatial econometrics and endemiology. In this work, we propose a class of penalized robust regression estimators based on exponential squared loss with independent and identical distributed errors for general spatial autoregressive models. A penalized exponential squared loss with the adaptive lasso penalty is employed for simultaneous model selection and parameter estimation. Under mild conditions, we establish the asymptotic and oracle property of the proposed estimators The induced nonconvex nondifferentiable mathematical programming offer challenges for solving algorithms. We specially design a block coordinate descent (BCD) algorithm equipped with CCCP procedure for efficiently solving the subproblem. Moreover, we provide a convergence guarantee of the BCD algorithm. Every limit point of the iterated solutions is proved a stationary point. We also present a convergence speed of spatial weight rho(k). Numerical studies illustrate that the proposed method is particularly robust and applicable when the outliers or intensive noise exist in the observations or the estimated spatial weight matrix is inaccurate. All the source code could be freely downloaded from https://github.com/Isaac-QiXing/SAR. (C) 2020 Elsevier B.V. All rights reserved.
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