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Quantile regression estimation of partially linear additive models

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  • Tadao Hoshino

Abstract

In this paper, we consider the estimation of partially linear additive quantile regression models where the conditional quantile function comprises a linear parametric component and a nonparametric additive component. We propose a two-step estimation approach: in the first step, we approximate the conditional quantile function using a series estimation method. In the second step, the nonparametric additive component is recovered using either a local polynomial estimator or a weighted Nadaraya-Watson estimator. Both consistency and asymptotic normality of the proposed estimators are established. Particularly, we show that the first-stage estimator for the finite-dimensional parameters attains the semiparametric efficiency bound under homoskedasticity, and that the second-stage estimators for the nonparametric additive component have an oracle efficiency property. Monte Carlo experiments are conducted to assess the finite sample performance of the proposed estimators. An application to a real data set is also illustrated.

Suggested Citation

  • Tadao Hoshino, 2014. "Quantile regression estimation of partially linear additive models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 509-536, September.
    • Handle: RePEc:taf:gnstxx:v:26:y:2014:i:3:p:509-536
    DOI: 10.1080/10485252.2014.929675
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    3. Seongil Jo & Taeyoung Roh & Taeryon Choi, 2016. "Bayesian spectral analysis models for quantile regression with Dirichlet process mixtures," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 177-206, March.
    4. Lebotsa, Moshoko Emily & Sigauke, Caston & Bere, Alphonce & Fildes, Robert & Boylan, John E., 2018. "Short term electricity demand forecasting using partially linear additive quantile regression with an application to the unit commitment problem," Applied Energy, Elsevier, vol. 222(C), pages 104-118.
    5. Cheng, Suli & Chen, Jianbao, 2023. "GMM estimation of partially linear additive spatial autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).
    6. Kellner, Ralf & Nagl, Maximilian & Rösch, Daniel, 2022. "Opening the black box – Quantile neural networks for loss given default prediction," Journal of Banking & Finance, Elsevier, vol. 134(C).

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