Abstract
Estimation of the extreme conditional quantiles with functional covariate is an important problem in quantile regression. The existing methods, however, are only applicable for heavy-tailed distributions with a positive conditional tail index. In this paper, we propose a new framework for estimating the extreme conditional quantiles with functional covariate that combines the nonparametric modeling techniques and extreme value theory systematically. Our proposed method is widely applicable, no matter whether the conditional distribution of a response variable Y given a vector of functional covariates X is short, light or heavy-tailed. It thus enriches the existing literature.
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References
Daouia, A., Gardes, L., Girard, S.: On kernel smoothing for extremal quantile regression. Bernoulli, 19, 2557–2589 (2013)
Daouia, A., Gardes, L., Girard, S., et al.: Kernel estimators of extreme level curves. TEST, 20, 311–333 (2011)
Davison, A. C., Ramesh, N. I.: Local likelihood smoothing of sample extremes. J. R. Stat. Soc. Ser. B, 62, 191–208 (2000)
Davison, A. C., Smith, R. L.: Models for exceedances over high thresholds. J. R. Stat. Soc. Ser. B, 52, 393–442 (1990)
De Haan, L., Ferreira, A.: Extreme Value Theory: An Introduction, Springer-Verlag, New York, 2006
Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis, Springer-Verlag, New York, 2006
Gardes, L., Girard, S., Lekina, A.: Functional nonparametric estimation of conditional extreme quantiles. J. Mult. Anal., 101, 419–433 (2010)
Gardes, L., Girard, S.: Functional kernel estimators of large conditional quantiles. Elec. J. Stat., 6, 1715–1744 (2012)
Gardes, L., Girard, S.: On the estimation of the functional Weibull tail-coefficient. J. Mult. Anal., 146, 29–45 (2016)
Hall, P., Tajvidi, N.: Nonparametric analysis of temporal trend when fitting parametric models to extremevalue data. Statist. Sci., 15, 153–167 (2000)
Resnick, S. I.: Extreme Values, Regular Variation and Point Processes, Springer-Verlag, New York, 1987
Smith, R. L.: Extreme value analysis of environmental time series: an application to trend detection in ground-level ozone. Statist. Sci., 4, 367–393 (1989)
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The authors thank the editor, the associate editor and two referees for their constructive comments that have led to a substantial improvement of the paper.
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Supported by the National Natural Science Foundation of China (Grant No. 11671338) and the Hong Kong Baptist University (Grant Nos. FRG1/16-17/018 and FRG2/16-17/074)
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He, F.Y., Cheng, Y.B. & Tong, T.J. Nonparametric Estimation of Extreme Conditional Quantiles with Functional Covariate. Acta. Math. Sin.-English Ser. 34, 1589–1610 (2018). https://doi.org/10.1007/s10114-018-7095-9
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DOI: https://doi.org/10.1007/s10114-018-7095-9