Distance-based regression model, as a nonparametric multivariate method, has been widely used to detect the association between variations in a distance or dissimilarity matrix for outcomes and predictor variables of interest in genetic association studies, genomic analyses, and many other research areas. Based on it, a pseudo-F statistic which partitions the variation in distance matrices is often constructed to achieve the aim. To the best of our knowledge, the statistical properties of the pseudo-F statistic has not yet been well established in the literature. To fill this gap, the authors study the asymptotic null distribution of the pseudo-F statistic and show that it is asymptotically equivalent to a mixture of chi-squared random variables. Given that the pseudo-F test statistic has unsatisfactory power when the correlations of the response variables are large, the authors propose a square-root F-type test statistic which replaces the similarity matrix with its square root. The asymptotic null distribution of the new test statistic and power of both tests are also investigated. Simulation studies are conducted to validate the asymptotic distributions of the tests and demonstrate that the proposed test has more robust power than the pseudo-F test. Both test statistics are exemplified with a gene expression dataset for a prostate cancer pathway.
In this paper, the L2,∞ normalization of the weight matrices is used to enhance the robustness and accuracy of the deep neural network(DNN) with Relu as activation functions. It is shown that the L2,∞ normalization leads to large dihedral angles between two adjacent faces of the DNN function graph and hence smoother DNN functions, which reduces over-fitting of the DNN. A global measure is proposed for the robustness of a classification DNN, which is the average radius of th... 相似文献
An ion flux dropout near the dipolarization front (DF) at around XGSM =- 11 RE in the Earth' s plasma sheet was observed by Time History of Events and Macroscale Interaction during substorms (THEMIS) on March 31, 2009. The ion differential energy fluxes at energies from 450 eV to 150 keV measured by the ESA and SST instruments from THC began to decrease about 2 s before the detection of the DF and reached a local minimum 6 s later. Then, the ion fluxes gradually increased to form a dropout around the DF. The spatial extent of the dropout was about 4,000 km. For energies above 20 keV, the ion fluxes after the dropout are greater than those before it, contrary to the fluxes at energies below 20 keV. The associated ion density variation indicates that the ion flux dropout coincides with the ion density dropout. Taking advantage of multipoint observations, THD, THC, and THE detected the same DF consecutively. Only THC detected an obvious ion flux dropout; THD observed an indistinct one about 2 s before THC; no high-energy (E 〉 30 keV) ion flux dropout was observed by THE. Our study suggests that the ion flux dropout may evolve with the earthward-propagating DF, and its properties can depend on locations relative to the DF. 相似文献