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Regression function comparison for paired data. (English) Zbl 1458.62155

Summary: In this paper, the regression function comparison for paired data is studied. The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses. There are several merits of the proposed statistic. For instance, it takes a simple \(V\)-statistic form. No bandwidth is needed. No moment conditions are required for covariates. It can be applied to covariates of any fixed dimension. The asymptotic results are also developed. It is proven that \(n\) times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives. Local alternative hypotheses which converge to the null hypothesis at the rate of \(n^{-1/2}\) are also detected. A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic. Simulation studies are carried out to illustrate the merits of the proposed method. A real data example is also used to illustrate the proposed testing procedures.

MSC:

62G08 Nonparametric regression and quantile regression
62G10 Nonparametric hypothesis testing
62G20 Asymptotic properties of nonparametric inference
62G09 Nonparametric statistical resampling methods
62P10 Applications of statistics to biology and medical sciences; meta analysis
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