Testing for additivity in nonparametric quantile regression

Dette, Holger; Guhlich, Matthias; Neumeyer, Natalie

doi:10.1007/s10463-014-0461-1

Cited by 2 publications

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“…These authors state that under the null hypothesis a normalized version of this test statistic converges weakly to a normal distribution (with rate n −1/2 g −d/4 n ). It should be pointed out here that the proof in this paper is not correct (see Dette et al 2012 for more details). Volgushev et al (2013) proposed a test for the hypothesis of the significance of the predictor Z in the nonparametric quantile regression model, which can detect local alternatives converging to the null hypothesis at a parametric rate and at the same time does not depend on the dimension of the predictor Z, such that smoothing with respect to the covariate Z can be avoided.…”

Section: Recent Goodness-of-fit Tests In Quantile Regressionmentioning

confidence: 82%

Comments on: An updated review of Goodness-of-Fit tests for regression models

Dette

2013

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A survey on the new developments in goodness-of-fit testing in regression models is very welcome and the authors have done an excellent job reviewing the recent literature. I would like to complement this nearly exhaustive exposition by focusing on two further issues in the context of testing model assumptions for regression models. The first refers to hypothesis testing in nonparametric quantile regression models, while the second discusses goodness-of-fit tests in inverse regression models. T and by Q(τ |x) = F −1 (y|x) the corresponding conditional quantile function. In the following we fix some quantile τ ∈ (0, 1). The recent literature on goodness-of-fit testing in quantile regression models discusses the problem of significance testing and testing for additivity. Both testing problems are motivated by the fact that in practical applications nonparametric quantile regression methods suffer from the curse of dimensionality and therefore do not yield precise estimates of conditional quantile surfaces for realistic sample sizes. Structural assumptions can improve the performance of estimators substantially. For example, under the additional assumption of additivity Recent goodness-of-fit tests in quantile regressionThis comment refers to the invited paper available at

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Section: Recent Goodness-of-fit Tests In Quantile Regressionmentioning

confidence: 82%