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Regression Function Comparison for Paired Data

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Abstract

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.

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Acknowledgements

The authors thank the editor, the associate editor and the anonymous referee for their constructive comments and suggestions that substantially improved an early manuscript.

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Authors and Affiliations

  1. School of Statistics, Beijing Normal University, Beijing, 100875, China

    Xu Guo

  2. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, China

    Jun Zhang

  3. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China

    Yun Fang

Authors
  1. Xu Guo
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  2. Jun Zhang
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  3. Yun Fang
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Corresponding author

Correspondence to Jun Zhang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11601227 and 11701034.

This paper was recommended for publication by Editor SHAO Jun.

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Guo, X., Zhang, J. & Fang, Y. Regression Function Comparison for Paired Data. J Syst Sci Complex 33, 1558–1570 (2020). https://doi.org/10.1007/s11424-020-8372-0

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  • DOI: https://doi.org/10.1007/s11424-020-8372-0

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