Variable selection for spatial semivarying coefficient models

Kangning Wang ()
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Kangning Wang: Shandong Technology and Business University

Annals of the Institute of Statistical Mathematics, 2018, vol. 70, issue 2, No 7, 323-351

Abstract: Abstract Spatial semiparametric varying coefficient models are a useful extension of spatial linear model. Nevertheless, how to conduct variable selection for it has not been well investigated. In this paper, by basis spline approximation together with a general M-type loss function to treat mean, median, quantile and robust mean regressions in one setting, we propose a novel partially adaptive group $$L_{r} (r\ge 1)$$ L r ( r ≥ 1 ) penalized M-type estimator, which can select variables and estimate coefficients simultaneously. Under mild conditions, the selection consistency and oracle property in estimation are established. The new method has several distinctive features: (1) it achieves robustness against outliers and heavy-tail distributions; (2) it is more flexible to accommodate heterogeneity and allows the set of relevant variables to vary across quantiles; (3) it can keep balance between efficiency and robustness. Simulation studies and real data analysis are included to illustrate our approach.

Keywords: Geostatistics; Variable selection; Robustness; Heterogeneity; Penalized M-type estimator; Oracle property (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10463-016-0589-2

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