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uniform confidence bands

ESAIM: Probability and Statistics (1)

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Uniform Confidence Bands for Local Polynomial Quantile Estimators ∗
Camille Sabbah
Journal:

ESAIM: Probability and Statistics / Volume 18 / 2014

Published online by Cambridge University Press:

25 July 2014, pp. 265-276

Print publication:

2014
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This paper deals with uniform consistency and uniform confidence bands for the quantile function and its derivatives. We describe a kernel local polynomial estimator of quantile function and give uniform consistency. Furthermore, we derive its maximal deviation limit distribution using an approximation in the spirit of Bickel and Rosenblatt [P.J. Bickel and M. Rosenblatt, Ann. Statist. 1 (1973) 1071–1095].