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 seve...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.展开更多
A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with...A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with rank higher than 2 is not available in the literature.We derive explicitly the asymptotic distribution of a degenerated U-statistic with any rank,which is useful for hypothesis testing when the test statistic is a degenerated U-statistic under null hypothesis.Interestingly,the limit for a degenerated U-statistic with rank higher than 2 is a weighted sum of independent polynomials of the standard normal random variables.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11601227and 11701034。
文摘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.
文摘A degenerated U-statistic with rank 2 is known to converge in distribution to a weighted sum of independent chi-square random variables.However,a result for the asymptotic distribution of a degenerated Ustatistic with rank higher than 2 is not available in the literature.We derive explicitly the asymptotic distribution of a degenerated U-statistic with any rank,which is useful for hypothesis testing when the test statistic is a degenerated U-statistic under null hypothesis.Interestingly,the limit for a degenerated U-statistic with rank higher than 2 is a weighted sum of independent polynomials of the standard normal random variables.
