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聚类相关数据的加权多元符号检验AI 解读

We consider the multivariate location problem with cluster-correlated data. A family of multivariate weighted sign tests is introduced for which observations from different clusters can receive different weights. Under weak assumptions, the test statistic is asymptotically distributed as a chi-squared random variable as the number of clusters goes to infinity. The asymptotic distribution of the test statistic is also given for a local alternative model under multivariate…

若干二维中位数的影响函数AI 解读

SUMMARY The asymptotic efficiency, influence function and breakdown properties of the multivariate median proposed by Oja are investigated and comparisons are made with two other generalizations of the median: the spatial median and the vector of marginal medians. It is shown that, for distributions with finite expectations, the Oja median has a bounded influence function although this median has 0% breakdown. For circular distributions, the influence functions of the Oja…

若干二元符号检验与中位数的性质AI 解读

Brown and Hettmansperger proposed an affine invariant bivariate analogue of the sign test, the OS test, based on the generalized median of Oja. On the other hand, Oja and Nyblom introduced a family of locally most powerful affine invariant sign tests. In the case of elliptic distributions, the locally most powerful Blumen's test and the OS test are shown to be asymptotically equivalent. Formulas for calculating asymptotic relative efficiencies of the OS test and the Oja…

多元正态情形下广义中位数的渐近性质AI 解读

SUMMARY The generalized affine invariant median proposed by Oja (1983) is, in the case of multivariate normality, shown to be asymptotically at least as efficient as the spatial median.