In this paper,we propose a novel approach to the multiple-sample testing problem using a studentized test statistic based on the random lifter technique.The method reformulates the classical Ksample test as an indepen...In this paper,we propose a novel approach to the multiple-sample testing problem using a studentized test statistic based on the random lifter technique.The method reformulates the classical Ksample test as an independence test between two random variables,enabling more efficient handling of complex data types.We solve problems with the non-standard normal limiting distributions of degenerate U-statistics using a random lifter approach.This creates a test statistic that is asymptotically normal under the null hypothesis.Numerous simulations and real-world applications have demonstrated that our method performs well with many data types,including Euclidean,directional,and symmetric positive definite data.It is also very good at controlling Type I errors.Our method also shows significant computational efficiency,outperforming existing K-sample tests,particularly when applied to large datasets.These results suggest that the proposed method is a powerful and practical solution for multiple-sample testing in complex data scenarios.展开更多
The pulse condition is an important basis for diagnosis and treatment intraditional Chinese medicine. From ancient times, Chinese physicians have been ableto make out the pathological changes of the nine organs by pul...The pulse condition is an important basis for diagnosis and treatment intraditional Chinese medicine. From ancient times, Chinese physicians have been ableto make out the pathological changes of the nine organs by pulse-feeling andpalpation, based on the theory that the pathological mystique lies in the pulsecondition. Chinese physicians have obtained and identified all along the pulsecondition by their finger tips, so there have been inevitably many subjective factors展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.12231017,72171216,71921001 and 71991474)the National Key R&D Program of China(Grant No.2022YFA1003803)supported by National Natural Science Foundation of China(Grant Nos.71873128 and 72293573).
文摘In this paper,we propose a novel approach to the multiple-sample testing problem using a studentized test statistic based on the random lifter technique.The method reformulates the classical Ksample test as an independence test between two random variables,enabling more efficient handling of complex data types.We solve problems with the non-standard normal limiting distributions of degenerate U-statistics using a random lifter approach.This creates a test statistic that is asymptotically normal under the null hypothesis.Numerous simulations and real-world applications have demonstrated that our method performs well with many data types,including Euclidean,directional,and symmetric positive definite data.It is also very good at controlling Type I errors.Our method also shows significant computational efficiency,outperforming existing K-sample tests,particularly when applied to large datasets.These results suggest that the proposed method is a powerful and practical solution for multiple-sample testing in complex data scenarios.
基金Project supported by the National Natural Science Foundation of China.
文摘The pulse condition is an important basis for diagnosis and treatment intraditional Chinese medicine. From ancient times, Chinese physicians have been ableto make out the pathological changes of the nine organs by pulse-feeling andpalpation, based on the theory that the pathological mystique lies in the pulsecondition. Chinese physicians have obtained and identified all along the pulsecondition by their finger tips, so there have been inevitably many subjective factors
