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对称分布混合模型的推断AI 解读

This article discusses the problem of estimation of parameters in finite mixtures when the mixture components are assumed to be symmetric and to come from the same location family. We refer to these mixtures as semi-parametric because no additional assumptions other than symmetry are made regarding the parametric form of the component distributions. Because the class of symmetric distributions is so broad, identifiability of parameters is a major issue in these mixtures. We…

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…

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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…

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…

基于稳健估计的残差：使用与解释AI 解读

Residual plots and diagnostic techniques are important tools for examining the fit of a regression model. In the case of least squares fits, plots of residuals provide a visual assessment of the adequacy of various aspects of the fitted model. An important question is whether plots of robust residuals can be interpreted in the same manner as their least squares counterparts. This article addresses this problem for two popular classes of robust estimates: M estimates and GM…

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基于秩的回归方法诊断AI 解读

Residual plots and diagnostic techniques have become important tools in examining the least squares fit of a linear model. In this article we explore the properties of the residuals from a rank-based fit of the model. We present diagnostic techniques that detect outlying cases and cases that have an influential effect on the rank-based fit. We show that the residuals from this fit can be used to detect curvature not accounted for by the fitted model. Furthermore, our…

基于单样本程序的删失生存时间中位数双样本推断AI 解读

Confidence intervals for median survival times are derived for censored survival data. The intervals are obtained by using the quantiles of the Kaplan-Meier product-limit estimator and have the same Pitman efficiency as the intervals found by inverting the sign test. Two-sample tests and confidence intervals for the difference in median survival times are then developed based on the comparison of the one-sample confidence intervals. Several methods for choosing the…

线性模型中的稳健有界影响检验AI 解读

A robust test that we call an aligned generalized M test for testing subhypotheses in general linear models is developed, and its asymptotic properties are studied. The test is a robustification of the well known F test, and it is an elegant alternative to Ronchetti's (1982) class of τ tests, p-values associated with it can be approximated readily using existing chi-square tables. The test is based on an appropriately constructed quadratic form and uses the generalized M…

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基于单样本符号统计量的两样本检验之Bahadur效率AI 解读

SUMMARY This paper discusses the two-sample test of location based on the comparison of two distribution-free one-sample confidence intervals derived from sign statistics. This test procedure, first introduced by Hettmansperger (1984), rejects the null hypothesis of equal population medians when the two intervals are disjoint. He presents three different ways to select the two one-sample intervals and one choice leads to Mood's test. All solutions have the same Pitman…

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多样本问题中模式化备择的检验AI 解读

This article suggests nonparametric methods of testing for a patterned alternative. As an example, suppose that we suspect that with increasing age, one's ability to perform a certain job tends to improve, but that after some point advancing age tends to mean diminishing performance. Suppose that N employees are grouped by age into k groups and employees' job performances are ranked from 1 to N. Viewing performance as the dependent variable, the particular pattern of…

线性模型中基于秩的推断的几何解释AI 解读

Four different approaches, based on ranks, to testing hypotheses are unified through the geometry of the linear model. The various tests are identified with different but algebraically equivalent forms of the classical F test. Small sample differences are investigated via a Monte Carlo study using both rank and signed rank tests.

基于简单秩阶梯得分统计量的位置模型推断AI 解读

A class of estimation procedures that are robust, relatively efficient, and yet computationally simple is proposed for the one- and two-sample location problems. Particular emphasis is placed on the problem of determining confidence intervals, a topic that has seen limited exposure in the literature. As a by-product, some interesting point estimates are obtained. A class of score functions that are ordinary step functions is considered for the location model. Point estimates…

基于简单秩阶梯得分统计量的位置模型推断AI 解读

A class of estimation procedures that are robust, relatively efficient, and yet computationally simple is proposed for the one- and two-sample location problems. Particular emphasis is placed on the problem of determining confidence intervals, a topic that has seen limited exposure in the literature. As a by-product, some interesting point estimates are obtained. A class of score functions that are ordinary step functions is considered for the location model. Point estimates…

单样本与双样本尺度模型的稳健估计和检验AI 解读

The purpose of this paper is to investigate the scale problem and develop a class of robust techniques which are useful in estimation and testing. The classical functional which has been used as a measure of variability of a distribution is the standard deviation. Its associated estimator, the sample standard deviation, is shown to have highly undesirable robustness properties. Another measure of variability, the square root of the midvariance, is proposed and investigated.…

单样本与双样本尺度模型的稳健估计和检验AI 解读

The purpose of this paper is to investigate the scale problem and develop a class of robust techniques which are useful in estimation and testing. The classical functional which has been used as a measure of variability of a distribution is the standard deviation. Its associated estimator, the sample standard deviation, is shown to have highly undesirable robustness properties. Another measure of variability, the square root of the midvariance, is proposed and investigated.…

多元位置参数的一类稳健检验与估计AI 解读

Hotelling's T 2 test and the sample mean vector for multivariate location suffer from the same lack of robustness as the univariate t test and sample mean. We propose a class of tests and estimates based on a vector of rank statistics and show that they are easy to compute, have good robustness properties, and are usually more efficient than the classical procedures.

多元位置参数的一类稳健检验与估计AI 解读

Hotelling's T 2 test and the sample mean vector for multivariate location suffer from the same lack of robustness as the univariate t test and sample mean. We propose a class of tests and estimates based on a vector of rank statistics and show that they are easy to compute, have good robustness properties, and are usually more efficient than the classical procedures.

基于似然比准则的稳健方差分析AI 解读

Robust tests of general linear hypotheses in linear models are developed. These are likelihood ratio type tests in the same sense that M -estimates are maximum likelihood type estimates. Construction of the tests suggests a decomposition of the data into terms analogous to classical sums of squares, providing a robust analysis of variance. Asymptotic efficiency and robustness properties of the tests are the same as those of the M -estimates upon which they are based.