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聚类多元数据的非参数分析AI 解读

There is wide interest in extending univariate and multivariate nonparametric procedures to clustered and hierarchical data. Traditionally, parametric mixed models have been used to account for the correlation structures among the dependent observational units. In this work we extend multivariate nonparametric procedures for one-sample and several-sample location problems to clustered data settings. The results are given for a general score function, but with an emphasis on…

形状矩阵的半参数有效秩推断（二）：最优 R 估计AI 解读

A class of R-estimators based on the concepts of multivariate signed ranks and the optimal rank-based tests developed in Hallin and Paindaveine [Ann. Statist. 34 (2006) 2707–2756] is proposed for the estimation of the shape matrix of an elliptical distribution. These R-estimators are root-n consistent under any radial density g, without any moment assumptions, and semiparametrically efficient at some prespecified density f. When based on normal scores, they are uniformly…

多变量独立性的非参数检验AI 解读

New test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines…

基于 zonotope 的散布矩阵估计AI 解读

We introduce a new scatter matrix functional which is a multivariate affine equivariant extension of the mean deviation $E(|x-\mbox{Med}(x)|)$. The estimate is constructed using the data vectors (centered with the multivariate Oja median) and their angular distances. The angular distance is based on Randles interdirections. The new estimate is called the zonoid covariance matrix (the ZCM), as it is the regular covariance matrix of the centers of the facets of the zonotope…

基于提升秩协方差矩阵的回归系数估计AI 解读

We introduce a new equivariant estimation method of the parameters of the multivariate regression model with q responses and p regressors. The estimate matrix is derived from the lift rank covariance matrix (LRCM) where the lift rank vectors are based on the Oja criterion function. The k = p + q variate ranks and k + 1 variate lift ranks are constructed using hyperplanes (or fits) going through k observations. The new LRCM regression estimate and the least squares (LS)…

基于符号协方差矩阵的回归系数估计AI 解读

Summary A new estimator of the regression parameters is introduced in a multivariate multiple-regression model in which both the vector of explanatory variables and the vector of response variables are assumed to be random. The affine equivariant estimate matrix is constructed using the sign covariance matrix (SCM) where the sign concept is based on Oja's criterion function. The influence function and asymptotic theory are developed to consider robustness and limiting…

仿射不变的多元单样本符号秩检验AI 解读

Brown and Hettmansperger introduced affine-invariant bivariate analogs of the sign, rank, and signed-rank tests based on the Oja median. In this article affine-invariant k-variate extensions of the one-sample signed-rank test and the Hodges-Lehmann estimate are considered. The necessary distribution theory is developed, and asymptotic Pitman efficiencies with respect to Hotelling's T 2 test under multivariate t distributions are tabulated. An application of the signed-rank…

多元空间符号与秩检验的效率AI 解读

Asymptotic Pitman efficiencies of multivariate spatial sign and rank methods are considered in the one-sample location case. Limiting distributions of the spatial sign and signed-rank tests under the null hypothesis as well as under contiguous sequences of alternatives are given. Formulae for asymptotic relative efficiencies are found and, under multivariate t distributions, relative efficiencies with respect to Hotelling's $T^2$ test are calculated.

仿射不变的多元多样本符号检验AI 解读

SUMMARY Invariant sign-type tests for the multivariate, multisample location models are developed. The definition of sign is based on the Oja criterion function. Emphasis is on the two-sample location model and the associated equivariant estimate of shift. Asymptotic theory is developed to provide large sample approximations for the null distribution of the test and to provide a framework for a discussion of efficiency. Tests are then developed for the one-way and two-way…

仿射不变的多元单样本符号检验AI 解读

SUMMARY Brown and Hettmansperger introduced an affine invariant bivariate analogue of the sign test based on the generalized median of Oja. In this paper its general multivariate extension is presented. The proposed multivariate permutation or sign change test is affine invariant with an easily computable covariance matrix. For elliptic distributions the proposed test and Randles's test are asymptotically equivalent. Formulae for calculating asymptotic relative efficiencies…

二元符号检验AI 解读

In this article the bivariate location problem is treated. New appealing bivariate analogs of the univariate sign tests are proposed for testing the null hypothesis concerning the unknown symmetry center. These tests remain unaltered under any nonsingular linear transformation. From these promising findings a whole family of locally most powerful invariant sign tests is introduced. The tests proposed earlier (Blumen 1958; Hodges 1955) are specific members of this family. For…

新的正态性检验AI 解读

A family of statistics for testing normality is presented which includes new tests for skewness, kurtosis and bimodality alternatives. The tests are simple to use and their power properties seem to be as good as those of the very similar U-statistics given by Oja (1981).

新的正态性检验AI 解读

A family of statistics for testing normality is presented which includes new tests for skewness, kurtosis and bimodality alternatives. The tests are simple to use and their power properties seem to be as good as those of the very similar U-statistics given by Oja (1981).

摘要暂缺

两种不依赖位置与尺度的拟合优度检验AI 解读

Location and scale-free goodness-of-fit tests based on new orderings of skewness and kurtosis are introduced. Davis & Quade (1978) have presented the test statistics earlier but they did not study their properties in testing goodness-of-fit. A combined test is also given. Some Monte Carlo comparisons show that the new tests have good power properties for testing normality.