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Regression Function Comparison for Paired Data
Journal of Systems Science and Complexity ( IF 2.1 ) Pub Date : 2020-04-30 , DOI: 10.1007/s11424-020-8372-0
Xu Guo , Jun Zhang , Yun Fang

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 n1/2 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.



中文翻译:

配对数据的回归函数比较

本文研究了配对数据的回归函数比较。拟议的测试统计量基于以响应差异为特征的特征函数的加权积分。提议的统计有很多优点。例如,它采用简单的V统计形式。不需要带宽。协变量不需要矩条件。它可以应用于任何固定维度的协变量。渐近结果也得到了发展。事实证明,在零假设下,n次拟议的检验统计量收敛到一个有限的极限,并且检验与任何固定的替代方案都一致。局部替代假设以n1/2的速率收敛到原假设也被检测到。还提出了合适的Bootstrap算法来实现所提出的测试统计量。仿真研究表明了该方法的优点。一个真实的数据示例也用于说明建议的测试过程。

更新日期:2020-04-30
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