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Abstract
This article proposes a new approach for testing the equality of nonparametric quantile regression functions based on marked empirical processes. We develop test statistics that posses better Type I and power properties in comparison to all available procedures in the literature. Simulation results also indicate that our tests have superior local power properties over existing tests. A data analysis is given which highlights the usefulness of the proposed methodology.
Highlights
Comparing groups based on independent samples has been a fundamental problem in statistics
This article proposes a new approach for testing the equality of nonparametric quantile regression functions based on marked empirical processes
We model gτ(·) nonparametrically with the following nonparametric quantile regression model: Yi j = gτ,i(Xi j) + i j, i = 1, . . . , k, j = 1, . . . , ni where gτ,i is the τth conditional quantile function of Y given X for the ith group and i j is a sequence of independent random variables assumed to be identically distributed within each group
Summary
Comparing groups based on independent samples has been a fundamental problem in statistics. Our method uses nonparametric quantile regression functions to construct test statistics that can detect differences at targeted quantiles in two or more conditional distributions. Sun (2006) and Dette, Wagner, and Volgushev (2011) have compared nonparametric quantile regression functions in the form of the above hypothesis The former propose a test based on an orthogonal moment condition of residuals which holds under the null hypothesis and the latter uses a test derived from the L2 distance of the etostitmheatneudllquatanatirlaetreeg( r√ensshi1o/n4)c−u1rwveisth.
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