Confidence intervals for nonparametric quantile regression: an emphasis on smoothing splines approach

E-ISSN： 1467-842x|59|4|527-543

ISSN： 1369-1473

Source： Australian & New Zealand Journal Of Statistics, Vol.59, Iss.4, 2017-12, pp. : 527-543

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Abstract

SummaryIn this paper we consider the problem of constructing confidence intervals for nonparametric quantile regression with an emphasis on smoothing splines. The mean‐based approaches for smoothing splines of Wahba (1983) and Nychka (1988) may not be efficient for constructing confidence intervals for the underlying function when the observed data are non‐Gaussian distributed, for instance if they are skewed or heavy‐tailed. This paper proposes a method of constructing confidence intervals for the unknown τth quantile function (0<τ<1) based on smoothing splines. In this paper we investigate the extent to which the proposed estimator provides the desired coverage probability. In addition, an improvement based on a local smoothing parameter that provides more uniform pointwise coverage is developed. The results from numerical studies including a simulation study and real data analysis demonstrate the promising empirical properties of the proposed approach.

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