The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space $\overline M $ (which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills field F j...The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space $\overline M $ (which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills field F jk on $\overline M $ . It is proved that both F jk and the invariant metric tensor g jk of $\overline M $ satisfy the Einstein-Yang-Mills equation. The case of N → ∞ is also discussed.展开更多
This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that ...This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.展开更多
基金This work was partially supported by the Ministry of Science and Technology, the National Natural Science Foundation of China (Grant No.19631010) Fundamental Research Bureau of CAS.
文摘The method used to construct the SU(2) Yang-Mills field on a compactified Minkowski space $\overline M $ (which is equivalent to the conformal space) is generalized to construct an SU(N)(N > 2) Yang-Mills field F jk on $\overline M $ . It is proved that both F jk and the invariant metric tensor g jk of $\overline M $ satisfy the Einstein-Yang-Mills equation. The case of N → ∞ is also discussed.
基金supported by National Natural Science Foundation of China (Grant Nos. 11071022, 11231010 and 11471223)Beijing Center for Mathematics and Information Interdisciplinary ScienceKey Project of Beijing Municipal Educational Commission (Grant No. KZ201410028030)
文摘This paper aims to develop a new robust U-type test for high dimensional regression coefficients using the estimated U-statistic of order two and refitted cross-validation error variance estimation. It is proved that the limiting null distribution of the proposed new test is normal under two kinds of ordinary models.We further study the local power of the proposed test and compare with other competitive tests for high dimensional data. The idea of refitted cross-validation approach is utilized to reduce the bias of sample variance in the estimation of the test statistic. Our theoretical results indicate that the proposed test can have even more substantial power gain than the test by Zhong and Chen(2011) when testing a hypothesis with outlying observations and heavy tailed distributions. We assess the finite-sample performance of the proposed test by examining its size and power via Monte Carlo studies. We also illustrate the application of the proposed test by an empirical analysis of a real data example.
