We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elemen...We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elements from arbitrary separable Hilbert spaces.This measure ex-tends the Kernel-based Conditional Mean Dependence.As the estimator of the measure is developed,the concentration property of the estimator is proved.Numerical results demonstrate the effectiveness of the new dependence meas-ure in the context of dependence testing,highlighting their advantages in cap-turing nonlinear partial conditional mean dependencies.展开更多
We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negat...We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.展开更多
This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable.A local influence detection approach is developed combining with the martingale...This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable.A local influence detection approach is developed combining with the martingale difference divergence(MDD)metric,and an efficient wild bootstrap implementation is given.The obtained new metric of the conditional mean dependence holds the merits of MDD,while it is more sensitive than the original one,and leads to a powerful test to nonlinear relationships.It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings.Theoretical asymptotic properties of the local influence test statistic are given,and a real data analysis is also presented for further illustration.The localization idea could be combined with other conditional mean dependence metrics.展开更多
This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determ...This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method.展开更多
This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional m...This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula(CC-SIS,for short).The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation,conditional mean and distance correlation(SIS,SIRS and DC-SIS,for short)and can significantly improve the performance of feature screening.We establish the sure screening property for the CC-SIS,and conduct simulations to examine its finite sample performance.Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models.At last,we also illustrate the CC-SIS through a real data example.展开更多
A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogen...A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.展开更多
文摘We introduce the Kernel-based Partial Conditional Mean Dependence,a sca-lar-valued measure of conditional mean dependence of Y given X,while adjusting for the nonlinear dependence on Z.Here X,Y and Z are random elements from arbitrary separable Hilbert spaces.This measure ex-tends the Kernel-based Conditional Mean Dependence.As the estimator of the measure is developed,the concentration property of the estimator is proved.Numerical results demonstrate the effectiveness of the new dependence meas-ure in the context of dependence testing,highlighting their advantages in cap-turing nonlinear partial conditional mean dependencies.
基金Acknowledgements The authors thank Editor Lu and two anonymous referees for their constructive suggestions and comments which helped in significantly improving an earlier version of this paper. This work is supported by the National Natural Science Foundation of China （11171001, 11201001, 11426032）, the Natural Science Foundation of Anhui Province （1308085QA03, 1408085QA02）, the Science Fund for Distinguished Young Scholars of Anhui Province （1508085J06）, and Introduction Projects of Anhui University Academic and Technology Leaders.
文摘We give the conditionally residual h-integrability with exponent r for an array of random variables and establish the conditional mean convergence of conditionally negatively quadrant dependent and conditionally negative associated random variables under this integrability. These results generalize and improve the known ones.
基金supported by the Project of Improving the Basic Scientific Research Ability of Young andMiddle-aged College Teachers in Guangxi(2023KY0058)the National Natural Science Foundation of China(No.12271014 and No.11971045).
文摘This article is focused on the problem to measure and test the conditional mean dependence of a response variable on a predictor variable.A local influence detection approach is developed combining with the martingale difference divergence(MDD)metric,and an efficient wild bootstrap implementation is given.The obtained new metric of the conditional mean dependence holds the merits of MDD,while it is more sensitive than the original one,and leads to a powerful test to nonlinear relationships.It is shown by simulations that the proposed test can achieve higher power for general conditional mean dependence relationships even in high-dimensional settings.Theoretical asymptotic properties of the local influence test statistic are given,and a real data analysis is also presented for further illustration.The localization idea could be combined with other conditional mean dependence metrics.
基金supported by the Aeronautical Science Foundation of China(20155553039)the Natural Sciences and Engineering Research Council of Canada(RGPIN 121384-11)
文摘This paper proposes a health evaluation method for degrading systems subject to competing risks of dependent soft and hard failures. To characterize the time-varying degradation rate, the degradation process is determined by a non-stationary Gamma process and the soft failure is encountered when it exceeds a predefined critical level. For the hard failure, a Cox’s proportional hazard model is applied to describe the hazard rate of the time to system failure. The dependent relationship is modeled by incorporating the degradation process as a time-varying covariate into the Cox’s proportional hazard model. To facilitate the health characteristics evaluation, a discretization technique is applied both to the degradation process and the monitoring time.All health characteristics can be obtained in the explicit form using the transition probability matrix, which is computationally attractive for practical applications. Finally, a numerical analysis is carried out to show the effectiveness and the performance of the proposed health evaluation method.
基金Supported by Natural Science Foundation of Henan(Grant No.202300410066)Program for Science and Technology Development of Henan Province(Grant No.242102310350).
文摘This paper is concerned with ultrahigh dimensional data analysis,which has become increasingly important in diverse scientific fields.We develop a sure independence screening procedure via the measure of conditional mean dependence based on Copula(CC-SIS,for short).The CC-SIS can be implemented as easily as the sure independence screening procedures which respectively based on the Pearson correlation,conditional mean and distance correlation(SIS,SIRS and DC-SIS,for short)and can significantly improve the performance of feature screening.We establish the sure screening property for the CC-SIS,and conduct simulations to examine its finite sample performance.Numerical comparison indicates that the CC-SIS performs better than the other two methods in various models.At last,we also illustrate the CC-SIS through a real data example.
文摘A weak type endpoint estimate for the maximal multilinear singular integral operator TAf（x）=supε〉0｜∫｜x-y｜〉εΩ（x-y）/｜x-y｜^n＋1（A（x）-A（y）-VA（y）（x-y））f（y）dy｜ is established, where Ω is homogeneous of degree zero, integrable on the unit sphere and has vanishing moment of order one, and A has derivatives of order one in BMO（R^n）. A regularity condition on Ω which implies an LlogL type estimate of TA is given.
