Robust variable selection with exponential squared loss for the partially linear varying coefficient spatial autoregressive model

Jialei Yu1,2, Yunquan Song1, Jiang Du2
1College of Science, China University of Petroleum, Qingdao, China
2Faculty of Science, Beijing University of Technology, Beijing, China

Tóm tắt

The partially linear varying coefficient spatial autoregressive model is a semi-parametric spatial autoregressive model in which the coefficients of some explanatory variables are variable, while the coefficients of the remaining explanatory variables are constant. For the nonparametric part, a local linear smoothing method is used to estimate the vector of coefficient functions in the model, and, to investigate its variable selection problem, this paper proposes a penalized robust regression estimation based on exponential squared loss, which can estimate the parameters while selecting important explanatory variables. A unique solution algorithm is composed using the block coordinate descent (BCD) algorithm and the concave-convex process (CCCP). Robustness of the proposed variable selection method is demonstrated by numerical simulations and illustrated by some housing data from Airbnb.

Tài liệu tham khảo

Beck A, Teboulle M (2009) A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J Imaging Sci 2(1):183–202 Cliff A, Ord J (1973) Spatial autocorrelation. Pion. Progress in Human Geography, London, pp 245–249 Fan J, Li R (2001) Variable selection via nonconcave penalized likelihood and its oracle properties. Publ Am Stat Assoc 96(456):1348–1360 Forsythe GE, Moler CB, Malcolm MA (1977) Computer methods for mathematical computations. Prentice-hall, Hoboken Guo S, Wei CH (2015) Variable selection for spatial autoregressive models. J Minzu Univ China (Nat Sci Ed) Kelejian HH (2008) A spatial j-test for model specification against a single or a set of non-nested alternatives. Lett Spat Resour Sci 1(1):3–11 Kelejian HH, Piras G (2011) An extension of Kelejian’s j-test for non-nested spatial models. Reg Sci Urban Econ 41(3):281–292 Kelejian HH, Piras G (2014) An extension of the j-test to a spatial panel data framework. J Appl Econom 31(2):387–402 Li T, Yin Q, Peng J (2020) Variable selection of partially linear varying coefficient spatial autoregressive model. J Stat Comput Simul 90(15):2681–2704 Liu X, Chen J, Cheng S (2018) A penalized quasi-maximum likelihood method for variable selection in the spatial autoregressive model. Spat Stat 25:86–104 Ma Y, Pan R, Zou T, Wang H (2020) A naive least squares method for spatial autoregression with covariates. Stat Sin 30(2):653–672 Mu J, Wang G, Wang L (2020) Spatial autoregressive partially linear varying coefficient models. J Nonparametric Stat 32(2):428–451 Song Y, Liang X, Zhu Y, Lin L (2021) Robust variable selection with exponential squared loss for the spatial autoregressive model. Comput Stat Data Anal 155(1):107094 Su L, Jin S (2010) Profile quasi-maximum likelihood estimation of partially linear spatial autoregressive models. J Econom 157(1):18–33 Tibshirani R (1996) Regression shrinkage and selection via the lasso. J R Stat Soc Ser B 58(1):267–288 Wang H, Li G, Jiang G (2007) Robust regression shrinkage and consistent variable selection through the lad-lasso. J Bus Econ Stat 25(3):347–355 Wang X, Jiang Y, Huang M, Zhang H (2013) Robust variable selection with exponential squared loss. JASA: J Am Stat Assoc 108:632–643 Yuille AL, Rangarajan A (2003) The concave-convex procedure. Neural Comput 15(4):915–936 Zhang X, Yu J (2018) Spatial weights matrix selection and model averaging for spatial autoregressive models. J Econom 203(1):1–18