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Variable selection for spatial semivarying coefficient models

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  • Kangning Wang

    (Shandong Technology and Business University
    Shandong University)

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.

Suggested Citation

  • Kangning Wang, 2018. "Variable selection for spatial semivarying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(2), pages 323-351, April.
    • Handle: RePEc:spr:aistmt:v:70:y:2018:i:2:d:10.1007_s10463-016-0589-2
    DOI: 10.1007/s10463-016-0589-2
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