Far East Journal of Theoretical Statistics
Volume 38, Issue 2, Pages 125 - 153
(February 2012)
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RATE OF STRONG UNIFORM CONSISTENCY FOR THE NONPARAMETRIC CONDITIONAL QUANTILE WITH DEPENDENT FUNCTIONAL DATA
Mostefa El Bahi
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Abstract: Let be a vector of random variables (rv’s), where T and X are, respectively, the interest variable and a covariate. In this paper, we study the nonparametric conditional quantile estimation for dependent functional data. Under some regularity conditions, the uniform strong convergence with rate of our estimator is established. We recover the rate of convergence in the known case of independent functional data. |
Keywords and phrases: dependent functional data, conditional quantile, kernel estimator, concentration measure, Kolmogorov's entropy. |
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