Uniform Confidence Bands for Local Polynomial Quantile Estimators
ESAIM: Probability and Statistics, Tome 18 (2014), pp. 265-276

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].

DOI : 10.1051/ps/2013035
Classification : 62G08, 62G15
Keywords: uniform confidence bands, conditional quantile estimation 
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     author = {Sabbah, Camille},
     title = {Uniform {Confidence} {Bands} for {Local} {Polynomial} {Quantile} {Estimators}},
     journal = {ESAIM: Probability and Statistics},
     pages = {265--276},
     year = {2014},
     publisher = {EDP Sciences},
     volume = {18},
     doi = {10.1051/ps/2013035},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ps/2013035/}
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Sabbah, Camille. Uniform Confidence Bands for Local Polynomial Quantile Estimators. ESAIM: Probability and Statistics, Tome 18 (2014), pp. 265-276. doi: 10.1051/ps/2013035

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