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High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression

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  • Carlos Martins-Filho
  • Feng Yao
  • Maximo Torero

Abstract

We consider the estimation of a high order quantile associated with the conditional distribution of a regressand in a nonparametric regression model. Our estimator is inspired by Pickands (1975) where it is shown that arbitrary distributions which lie in the domain of attraction of an extreme value type have tails that, in the limit, behave as generalized Pareto distributions (GPD). Smith (1987) has studied the asymptotic properties of maximum likelihood (ML) estimators for the parameters of the GPD in this context, but in our paper the relevant random variables used in estimation are standardized residuals from a first stage kernel based nonparametric estimation. We obtain convergence in probability and distribution of the residual based ML estimator for the parameters of the GPD as well as the asymptotic distribution for a suitably defined quantile estimator. A Monte Carlo study provides evidence that our estimator behaves well in finite samples and is easily implementable. Our results have direct application in finance, particularly in the estimation of conditional Value-at-Risk, but other researchers in applied fields such as insurance will also find the results useful.

Suggested Citation

  • Carlos Martins-Filho & Feng Yao & Maximo Torero, 2015. "High-Order Conditional Quantile Estimation Based on Nonparametric Models of Regression," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 907-958, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:907-958
    DOI: 10.1080/07474938.2014.956612
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    References listed on IDEAS

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    1. Cai, Zongwu & Wang, Xian, 2008. "Nonparametric estimation of conditional VaR and expected shortfall," Journal of Econometrics, Elsevier, vol. 147(1), pages 120-130, November.
    2. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, Decembrie.
    3. Victor Chernozhukov, 2005. "Extremal quantile regression," Papers math/0505639, arXiv.org.
    4. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
    5. Carlos Martins-Filho & Feng Yao, 2006. "A Note on the Use of V and U Statistics in Nonparametric Models of Regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 389-406, June.
    6. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    7. Martins-Filho, Carlos & Yao, Feng, 2008. "A smooth nonparametric conditional quantile frontier estimator," Journal of Econometrics, Elsevier, vol. 143(2), pages 317-333, April.
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    Cited by:

    1. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    2. Matthias Kalkuhl & Lukas Kornher & Marta Kozicka & Pierre Boulanger & Maximo Torero, 2013. "Conceptual framework on price volatility and its impact on food and nutrition security in the short term," FOODSECURE Working papers 15, LEI Wageningen UR.
    3. Matthias Kalkuhl & Mekbib Haile & Lukas Kornher & Marta Kozicka, 2015. "Cost-benefit framework for policy action to navigate food price spikes. FOODSECURE Working Paper No 33," FOODSECURE Working papers 33, LEI Wageningen UR.
    4. Almanzar, Miguel & Torero, Maximo, 2017. "Media Coverage and Food Commodities: Agricultural Futures Prices and Volatility Effects," Discussion Papers 264781, University of Bonn, Center for Development Research (ZEF).
    5. Kalkuhl, Matthias & von Braun, Joachim & Torero, Maximo, 2016. "Food Price Volatility and Its Implications for Food Security and Policy," MPRA Paper 72164, University Library of Munich, Germany.

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