Significance testing in quantile regression

2012/06/14 by Volgushev, Stanislav, Birke, Melanie, Dette, Holger +1
#FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1206.3125

Abstract

We consider the problem of testing significance of predictors in multivariate nonparametric quantile regression. A stochastic process is proposed, which is based on a comparison of the responses with a nonparametric quantile regression estimate under the null hypothesis. It is demonstrated that under the null hypothesis this process converges weakly to a centered Gaussian process and the asymptotic properties of the test under fixed and local alternatives are also discussed. In particular we show, that - in contrast to the nonparametric approach based on estimation of L²-distances - the new test is able to detect local alternatives which converge to the null hypothesis with any rate a_n → 0 such that a_n √(n) → ∞ (here n denotes the sample size). We also present a small simulation study illustrating the finite sample properties of a bootstrap version of the the corresponding Kolmogorov-Smirnov test.

Related

• Powerful nonparametric checks for quantile regression
• The independence process in conditional quantile location-scale models and an application to testing for monotonicity
• Global quantile regression
• Uniform Inference for High-dimensional Quantile Regression: Linear\n Functionals and Regression Rank Scores
• Quantile Processes for Semi and Nonparametric Regression