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Single index quantile regression for heteroscedastic data

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  • Christou, Eliana
  • Akritas, Michael G.

Abstract

Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. Linear and nonlinear QR models have been studied extensively, while recent research focuses on the single index quantile regression (SIQR) model. Compared to the single index mean regression (SIMR) problem, the fitting and the asymptotic theory of the SIQR model are more complicated due to the lack of closed form expressions for estimators of conditional quantiles. Consequently, the proposed methods are necessarily iterative. We propose a non-iterative estimation algorithm, and derive the asymptotic distribution of the proposed estimator under heteroscedasticity. For identifiability, we use a parametrization that sets the first coefficient to 1 instead of the typical condition which restricts the norm of the parametric component. This distinction is more than simply cosmetic as it affects, in a critical way, the correspondence between the estimator derived and the asymptotic theory.

Suggested Citation

  • Christou, Eliana & Akritas, Michael G., 2016. "Single index quantile regression for heteroscedastic data," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 169-182.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:169-182
    DOI: 10.1016/j.jmva.2016.05.010
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    Cited by:

    1. Rong Jiang & Mengxian Sun, 2022. "Single-index composite quantile regression for ultra-high-dimensional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 443-460, June.
    2. Eliana Christou & Annabel Settle & Andreas Artemiou, 2021. "Nonlinear dimension reduction for conditional quantiles," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 937-956, December.
    3. Zhao, Weihua & Zhou, Yan & Lian, Heng, 2018. "Time-varying quantile single-index model for multivariate responses," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 32-49.
    4. Eliana Christou & Michael G. Akritas, 2019. "Single index quantile regression for censored data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 655-678, December.
    5. Eliana Christou, 2020. "Robust dimension reduction using sliced inverse median regression," Statistical Papers, Springer, vol. 61(5), pages 1799-1818, October.
    6. Jiang, Rong & Yu, Keming, 2020. "Single-index composite quantile regression for massive data," Journal of Multivariate Analysis, Elsevier, vol. 180(C).

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