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更简便的仿射不变多元分布无关符号检验AI 解读

A simpler multivariate sign test is proposed that uses the transformation-retransformation approach of Chakraborty, Chaudhuri, and Oja together with a directional transformation due to Tyler. This produces a multivariate sign test that is practical to apply to data of any dimension, makes minimal assumptions about the underlying distribution, and has a small-sample distribution-free property over a broad class of population models. It is shown to perform very well in…

两个向量之间独立性的非参数检验AI 解读

A new statistic, [Qcirc] n , based on interdirections is proposed for testing whether two vector-valued quantities are dependent. The statistic, which has an intuitive invariance property, reduces to the quadrant statistic when the two quantities are each univariate. Under the null hypothesis of independence, [Qcirc] n has a limiting chi-squared distribution when each vector is elliptically symmetric. The new statistic is compared to the classical normal theory…

简单重复测量设计的方向间检验AI 解读

Interdirection tests are proposed for a simple repeated-measures design. The test statistics proposed are applications of the one-sample interdirection sign test and interdirection signed-rank test to a repeated-measurement setting. The interdirection sign test has a small-sample distribution-free property and includes the two-sided univariate sign test and Blumen's bivariate sign test as special cases. The interdirection signed-rank test includes the two-sided univariate…

两样本位置问题的二元符号秩检验AI 解读

SUMMARY A signed rank affine invariant test for the difference in location between two elliptically symmetric populations is proposed. Asymptotic properties of the test are developed under the null hypothesis and under contiguous alternatives. The proposed statistic is compared with three of its competitors using Monte Carlo studies and Pitman asymptotic relative efficiencies. It is seen that the signed rank statistic introduced is especially powerful when the underlying…

单样本多元位置问题的符号秩检验AI 解读

An affine-invariant signed-rank test is proposed for the one-sample multivariate location problem. The test suggested is a modification of Randles's multivariate sign test based on interdirections, which extends Blumen's bivariate procedure to the multidimensional setting. Comparisons are made between the proposed statistic and several competitors via Pitman asymptotic relative efficiencies and Monte Carlo results. The signed-rank statistic appears to be robust. It performs…

基于观测间方向计数的分布无关多元符号检验AI 解读

Distribution-free tests are investigated for the one-sample multivariate location problem. Counts, called interdirections, which measure the angular distance between two observation vectors relative to the positions of the other observations, are introduced. These counts are invariant under nonsingular linear transformations and have a small-sample distribution-free property over a broad class of population models, called distributions with elliptical directions, which…

代入参数估计量对卡方极限 U 与 V 统计量的影响AI 解读

Consider statistics $T_n(\lambda)$ that take the form of limiting chi-square (degenerate) $U$ or $V$ statistics. Here the phrase "limiting chi-square" means they have the same asymptotic distribution as a weighted sum of (possibly infinitely many) independent $\chi^2_1$ random variables. This paper examines the limiting distribution of $T_n(\hat{\lambda})$ and compares it to that of $T_n(\lambda)$, where $\hat{\lambda}$ denotes a consistent estimator of $\lambda$ based on…

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基于残差实施检验的渐近性质AI 解读

The null distribution of a test statistic computed on residuals can be affected by the dependence among the residuals. It might be expected, however, that the dependence decreases as the sample size increases, so that the limiting null distribution is the same as if the test were based on independent observations. The author investigates whether this large sample equivalence holds for tests of correlation, scale difference, regression, and location difference. Particular…

含估计参数的统计量的渐近正态性AI 解读

Often a statistic of interest would take the form of a member of a common family, except that some vital parameter is unknown and must be estimated. This paper describes methods for showing the asymptotic normality of such statistics with estimated parameters. Whether or not the limiting distribution is affected by the estimator is primarily a question of whether or not the limiting mean (derived by replacing the estimator by a mathematical variable) has a nonzero derivative…

检测二元总体的边际尺度差异AI 解读

A conditional test is proposed that uses the null hypothesis of bivariate symmetry to detect unequal marginal scales in a bivariate population. The asymptotic normality of the test statistic and the consistency of the test are established. Asymptotic relative efficiency comparisons are made with the standard parametric test in both the bivariate normal case and in a trivariate reduction model case and with two of Sen's (1967) tests in the bivariate normal case. The good…

摘要暂缺

对称性对非对称性的渐近分布无关检验AI 解读

An asymptotically distribution-free procedure is proposed for testing whether a univariate population is symmetric about some unknown value versus a broad class of asymmetric distribution alternatives. The consistency class of the test is discussed and two competing tests are described, one based on the sample skewness, and the other on Gupta's nonparametric procedure. A Monte Carlo study shows that the proposed test is superior to either competitor since it maintains the…

使用稳健估计的广义线性与二次判别函数AI 解读

Two new methods of constructing robust linear and quadratic discriminant functions are introduced. The first is a generalization of Fisher's procedure for finding a linear discriminant function. It places less weight on those observations that are far from the overlapping regions of the two populations. The second new method substitutes M-estimates of the means and the covariance matrices into the usual expressions for the linear and quadratic discriminant functions. Monte…

卡方拟合优度检验的功效近似：简单假设情形AI 解读

The limiting distribution of the chi-square goodness-of-fit statistic Tn under alternatives is noncentral chi-square if the alternative probabilities approach the null probabilities at an appropriate rate as n → ∞. It is shown that for fixed alternative probabilities, the limiting distribution of (Tn − μ n )/σ n is standard normal. Both of these asymptotic results can be used to approximate the power of the goodness-of-fit test. Numerical comparisons between these two…

无分布假设的部分判别分析AI 解读

A distribution-free rank procedure is proposed for use in partial discrimination problems involving two populations. It is shown that this procedure can be applied with virtually any discriminant function. Moreover, the discriminant function may be selected after observing the samples on which it is to be based. Using Monte Carlo methods the rank procedure is compared with a normal theory and a tolerance region procedure. The rank procedure was the only one that adequately…

两样本自适应无分布检验AI 解读

An adaptive distribution-free test is proposed for the two-sample location problem. First, the data are used to assess the tailweight and skewness of the underlying distributions. This leads to the selection and then application, with the same data, of one of several common rank tests for shift, such as the Mann-Whitney-Wilcoxon test. The preliminary selection is made in a way that insures the testing procedure is distribution-free. A Monte Carlo study shows that the…

底层分布的选择与自适应估计AI 解读

In our approach to adaptive inference, selection of the true underlying family of distributions is needed. A Bayesian selection rule, which is based on non-informative priors for the parameters, and a multiple decision solution, that maximizes the weighted sum of the probabilities of correct selection, are presented; both of these yield a decision rule of the same form. A modified maximum likelihood solution is also given and is used to construct an adaptive estimate of the…

若干不相关与独立的秩统计量AI 解读

Some interesting examples of uncorrelated simple linear rank statistics are listed. Consideration is then given to conditions under which general rank statistics are uncorrelated or have joint distributions which enjoy certain symmetric properties. Two simple linear rank statistics that are uncorrelated are found, under suitable restrictions, to be asymptotically independent. This is followed by some illustrations in which two rank statistics are exactly independent. The…