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一种实用的仿射等变多元中位数AI 解读

A robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one. The estimator is robust in the sense that it has a bounded influence function, a positive breakdown value and has high efficiency compared to the sample mean for heavy‐tailed distributions. Perhaps its greatest strength is that, unlike other affine equivariant multivariate medians, it is easily computed for data in any practical…

混合模型中重复测量的近乎非参数推断AI 解读

Summary We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The…

正态得分、正态概率图与正态性检验AI 解读

In this article we develop new plotting positions for normal plots. The use of the plots usually centers on detecting irregular tail behavior or outliers. Along with the normal plot, we develop tests for various departures from normality, especially for skewness and heavy tails. The tests can be considered as components of a Shapiro-Wilk type test that has been decomposed into different sources of nonnormality. Convergence to the limiting distributions is slow, so finite…

具有回降影响函数的正则秩估计AI 解读

A study is made of some unusual location estimates first proposed in 1977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established some strong robustness properties of these estimates, such as redescending influence functions and, in some cases, full efficiency at the Cauchy model. It is further shown here that the estimates, called M-W-S estimates, are derivable from a rank-based scheme founded on convex functions and hence are regular, are unique, and have…

正则的回降秩估计AI 解读

A study is made of some unusual location estimates first proposed in 1977 by J. S. Maritz, M. Wu, and R. G. Staudte, Jr., who established some strong robustness properties of these estimates, such as redescending influence functions and, in some cases, full efficiency at the Cauchy model. It is further shown here that the estimates, called M-W-S estimates, are derivable from a rank-based scheme founded on convex functions and hence are regular, are unique, and have…

SUMMARY When εi = yi – x′i β, it is known that minimizing ΣΣ|εi – εj| yields an estimate of regression that attains a bounded influence of the residual with 95% efficiency for the normal distribution. We show that introducing weights ΣΣbij|εi – εj| achieves bounded total influence with positive breakdown. Mallows weights in particular are optimally efficient under a predefined bound on the gross error sensitivity. A generalization of Mallows weights allows additional local…

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…

不要求总体分布形状的修正 Mood 位置检验AI 解读

In this paper an asymptotically distribution-free test is given for the difference of two location parameters without any shape assumptions on the underlying populations. In the past, conservative tests for this problem have been proposed. In the present paper we take the same approach and then alter the statistic with a consistent estimate of its variance under the null hypothesis.