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Non-parametric estimation of conditional quantiles

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  • Samanta, M.

Abstract

Let (X, Y) be a two dimensional random variable with a joint density function f(x, y) and a joint distribution function F(x, y) = [small esh]x-[infinity][small esh]y-[infinity]f(u, v) dv du. Following Nadaraya (1964) and Rosenblatt (1969) a class of nonparametric estimators of conditional quantiles of Y for a given value of X, based on a random sample from the above distribution, is proposed. It is shown that under some regularity conditions the estimators are strongly consistent and asymptotically normally distributed.

Suggested Citation

  • Samanta, M., 1989. "Non-parametric estimation of conditional quantiles," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 407-412, April.
    • Handle: RePEc:eee:stapro:v:7:y:1989:i:5:p:407-412
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    Cited by:

    1. Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    2. De Gooijer, Jan G. & Gannoun, Ali & Zerom, Dawit, 2002. "Mean squared error properties of the kernel-based multi-stage median predictor for time series," Statistics & Probability Letters, Elsevier, vol. 56(1), pages 51-56, January.
    3. Marcelo Fernandes & Emmanuel Guerre & Eduardo Horta, 2021. "Smoothing Quantile Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(1), pages 338-357, January.
    4. Zongwu Cai & Xian Wang, 2013. "Nonparametric Methods for Estimating Conditional VaR and Expected Shortfall," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    5. Chen, Yaqing & Dawson, Matthew & Müller, Hans-Georg, 2020. "Rank dynamics for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    6. Gannoun, Ali & Girard, Stephane & Guinot, Christiane & Saracco, Jerome, 2004. "Sliced inverse regression in reference curves estimation," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 103-122, May.
    7. Gardes, Laurent & Girard, Stéphane, 2016. "On the estimation of the functional Weibull tail-coefficient," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 29-45.
    8. Ioannides, D. A., 2004. "Fixed design regression quantiles for time series," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 235-245, July.
    9. Abberger, Klaus, 1994. "Nichtparametrische Schätzung bedingter Quantile in Finanzmarktdaten," Discussion Papers, Series II 225, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    10. Ould-SaI¨d, Elias, 2006. "A strong uniform convergence rate of kernel conditional quantile estimator under random censorship," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 579-586, March.
    11. Kadiri Nadia & Rabhi Abbes & Bouchentouf Amina Angelika, 2018. "Strong uniform consistency rates of conditional quantile estimation in the single functional index model under random censorship," Dependence Modeling, De Gruyter, vol. 6(1), pages 197-227, November.
    12. Hamri Mohamed Mehdi & Mekki Sanaà Dounya & Rabhi Abbes & Kadiri Nadia, 2022. "Single Functional Index Quantile Regression for Independent Functional Data Under Right-Censoring," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(1), pages 31-62, March.
    13. Daouia, Abdelaati & Gardes, Laurent & Girard, Stephane, 2011. "On kernel smoothing for extremal quantile regression," LIDAM Discussion Papers ISBA 2011031, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Ahmad Aboubacrène Ag & Deme El Hadji & Diop Aliou & Girard Stéphane, 2019. "Estimation of the tail-index in a conditional location-scale family of heavy-tailed distributions," Dependence Modeling, De Gruyter, vol. 7(1), pages 394-417, January.
    15. Girard, Stéphane & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Functional estimation of extreme conditional expectiles," Econometrics and Statistics, Elsevier, vol. 21(C), pages 131-158.
    16. Abdelaati Daouia & Laurent Gardes & Stéphane Girard & Alexandre Lekina, 2011. "Kernel estimators of extreme level curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 311-333, August.
    17. Laksaci, Ali & Lemdani, Mohamed & Ould-Sad, Elias, 2009. "A generalized L1-approach for a kernel estimator of conditional quantile with functional regressors: Consistency and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1065-1073, April.
    18. Lee, Tae-Hwy & Saltoglu, Burak, 2002. "Assessing the risk forecasts for Japanese stock market," Japan and the World Economy, Elsevier, vol. 14(1), pages 63-85, January.

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