Abstract
In this paper, we study an L 1-norm kernel estimator of the conditional quan- tile (CQ) of a scalar response variable Y given a random variable (rv) X taking values in a semi-metric space. The almost complete (a.co.) consis- tency and the asymptotic normality of this estimate are obtained when the sample is an α-mixing sequence. We illustrate our methodology by applying the estimator to climatological data.
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References
Bradley, R.C. (2007). Introduction to strong mixing conditions. Vol. I–III. Kendrick Press, Utah.
Doukhan, P., Massart, P. and Rio, E. (1994). The functional central limit theorem for strongly mixing processes. Ann. Inst. H. Poincar Probab. Statist., 30, 63–82.
Ezzahrioui, M. and Ould Saïd, E. (2008). Asymptotic results of a nonparametric conditional quantile estimator for functional time series data. Comm. Statist. Theory Methods. 37, 2735–2759.
Ferraty, F., Laksaci, A., Tadj, A. and Vieu, P. (2009). Rate of uniform consistency for nonparametric estimates with functional variables. J. Statist. Plann. Inference, 140, 335–352.
Ferraty, F., Mas, A. and Vieu, P. (2007). Nonparametric regression on functional data: inference and practical aspects. Aust. N. Z. J. Stat., 49, 267–286.
Ferraty, F., Rabhi, A. and Vieu, P. (2005). Conditional quantiles for functional dependent data with application to the climatic El Niño phenomenon. Sankhyā, 67, 378–398.
Ferraty, F. and Vieu, P. (2006). Nonparametric Functional Data Analysis. Theory and Practice. Springer-Verlag, New York.
Gannoun, A., Saracco, J. and Yu, K. (2003). Nonparametric prediction by conditional median and quantiles. J. Statist. Plann. Inference, 117, 207–223.
Laksaci, A., Lemdani, M. and Ould Saïd, E. (2009). L 1-norm kernel estimator of conditional quantile for functional regressors: consistency and asymptotic normality. Statist. Probab. Lett., 79, 1065–1073.
Lin, Z. and Li, D. (2007). Asymptotic normality for L 1-norm kernel estimator of conditional median under association dependence. J. Multivariate Anal., 98, 1214–1230.
Masry, E. (1986). Recursive probability density estimation for weakly dependent stationary processus. IEEE Trans. Inform. Theory, 32, 254–267.
Polonik, W. and Yao, Q. (2000). Conditional minimum volume predictive regions for stochastic processes. J. Amer. Statist. Assoc., 95, 509–519.
Rio, E. (2000). Théorie asymptotique des processus aléatoires faiblement dépendants (in French). Mathématiques et Applications, 31. Springer, Berlin.
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Laksaci, A., Lemdani, M. & Saïd, E.O. Asymptotic results for an L 1-norm kernel estimator of the conditional quantile for functional dependent data with application to climatology. Sankhya A 73, 125–141 (2011). https://doi.org/10.1007/s13171-011-0002-4
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DOI: https://doi.org/10.1007/s13171-011-0002-4