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High-dimensional quantile varying-coefficient models with dimension reduction

Author

Listed:
  • Weihua Zhao

    (Nantong University)

  • Rui Li

    (Shanghai University of International Business and Economics)

  • Heng Lian

    (City University of Hong Kong
    City University of Hong Kong Shenzhen Research Institute)

Abstract

Although semiparametric models, in particular varying-coefficient models, alleviate the curse of dimensionality by avoiding estimation of fully nonparametric multivariate functions, there would typically still be a large number of functions to estimate. We propose a dimension reduction approach to estimating a large number of nonparametric univariate functions in varying-coefficient models, in which these functions are constrained to lie in a finite-dimensional subspace consisting of the linear span of a small number of smooth functions. The proposed methodology is put in the context of quantile regression, which provides more information on the response variable than the more conventional mean regression. Finally, we present some numerical illustrations to demonstrate the performances.

Suggested Citation

  • Weihua Zhao & Rui Li & Heng Lian, 2022. "High-dimensional quantile varying-coefficient models with dimension reduction," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(1), pages 1-19, January.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:1:d:10.1007_s00184-021-00814-5
    DOI: 10.1007/s00184-021-00814-5
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    References listed on IDEAS

    as
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