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A new minimum contrast approach for inference in single-index models

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  • Li, Weiyu
  • Patilea, Valentin

Abstract

Semiparametric single-index models represent an appealing compromise between parametric and nonparametric approaches and have been widely investigated in the literature. The underlying assumption in single-index models is that the information carried by the vector of covariates could be summarized by a one-dimensional projection. We propose a new, general inference approach for such models, based on a quadratic form criterion involving kernel smoothing. The approach could be applied with general single-index assumptions, in particular for mean regression models and conditional law models. The covariates could be unbounded and no trimming is necessary. A resampling method for building confidence intervals for the index parameter is proposed. Our empirical experiments reveal that the new method performs well in practice.

Suggested Citation

  • Li, Weiyu & Patilea, Valentin, 2017. "A new minimum contrast approach for inference in single-index models," Journal of Multivariate Analysis, Elsevier, vol. 158(C), pages 47-59.
    • Handle: RePEc:eee:jmvana:v:158:y:2017:i:c:p:47-59
    DOI: 10.1016/j.jmva.2017.03.009
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    References listed on IDEAS

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    Cited by:

    1. Claudio Agostinelli & Ana M. Bianco & Graciela Boente, 2020. "Robust estimation in single-index models when the errors have a unimodal density with unknown nuisance parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 855-893, June.

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