Confidence corridors for multivariate generalized quantile regression
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Date
2014-05-21
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Abstract
We focus on the construction of confidence corridors for multivariate nonparametric
generalized quantile regression functions. This construction is based on asymptotic
results for the maximal deviation between a suitable nonparametric estimator and the
true function of interest which follow after a series of approximation steps including
a Bahadur representation, a new strong approximation theorem and exponential tail
inequalities for Gaussian random fields.
As a byproduct we also obtain confidence corridors for the regression function in the
classical mean regression. In order to deal with the problem of slowly decreasing error
in coverage probability of the asymptotic confidence corridors, which results in meager
coverage for small sample sizes, a simple bootstrap procedure is designed based on
the leading term of the Bahadur representation. The finite sample properties of both
procedures are investigated by means of a simulation study and it is demonstrated that
the bootstrap procedure considerably outperforms the asymptotic bands in terms of
coverage accuracy. Finally, the bootstrap confidence corridors are used to study the
efficacy of the National Supported Work Demonstration, which is a randomized employment
enhancement program launched in the 1970s. This article has supplementary
materials online.
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Keywords
smoothing and nonparametric regression, bootstrap, expectile regression, goodness-of-fit tests, quantile treatment effect