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圆周数据的时间序列分析AI 解读

SUMMARY The paper considers the problem of modelling and analysing a time series of measurements which take the form of unit two-dimensional vectors. Several general classes of existing and new models are studied in terms of feasibility and flexibility. An approach is recommended which uses two of these classes, and which takes advantage of several standard time series algorithms that are available in modern software packages. An application is given to the analysis of a…

球面中位轴AI 解读

SUMMARY In an earlier paper, Fisher defined the notion of a median direction for data from a unimodal distribution of three-dimensional unit vectors and studied its statistical properties. Corresponding notions of a median axis for bipolar axial or great circle data were also suggested but not analysed. This paper gives a statistical treatment of spherical median axes, including their asymptotic relative efficiencies, and a comparison with the customary principal or polar…

摘要暂缺

单位球面或超球面随机变量的相关系数AI 解读

A coefficient to measure association between two random variables, each distributed on the surface of the unit sphere in p-dimensional space, is proposed, analogous to an existing correlation coefficient for circular data. The sample estimate is studied in detail for the case p = 3, and comparisons are made with other statistics in current use. Some applications are given to studying remanent magnetization in rock samples.

单位球面或超球面随机变量的相关系数AI 解读

A coefficient to measure association between two random variables, each distributed on the surface of the unit sphere in p-dimensional space, is proposed, analogous to an existing correlation coefficient for circular data. The sample estimate is studied in detail for the case p = 3, and comparisons are made with other statistics in current use. Some applications are given to studying remanent magnetization in rock samples.

用于评估依赖关系的 χ 图AI 解读

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…

用于评估依赖关系的 Chi 图AI 解读

This paper presents a graphical method to be used, in conjunction with a scatterplot, to investigate possible association of two variates as manifested in a sample of bivariate measurements. The method is designed so that the plot is approximately horizontal under independence, and under various forms of association it produces corresponding characteristic patterns. Examples given include application to study of regression residuals, dependence of two spatial point…

圆周数据的相关系数AI 解读

SUMMARY A coefficient to measure association between angular variables is discussed, its asymptotic distribution found, and its properties developed. Comparisons with other statistics in current use are made, and some examples given.

摘要暂缺

若干非参数分布族的无偏估计AI 解读

This paper is concerned with the theory of unbiased estimation for nonparametric families of distributions subject to "generalised moment" restrictions. Necessary and sufficient conditions under which symmetric statistics are unique minimum variance unbiased estimators of their expectations are obtained, and some new boundedly complete families of distributions are exhibited.

角度变量与线性变量关联的非参数度量AI 解读

General models of association between an angular and a linear variable, corresponding to monotone association between two linear variables, are proposed; U-statistics which are analogues of Kendall's tau are developed to measure such association, their distributions obtained, and their performances compared with other measures of angular-linear association.

角度变量与线性变量关联的非参数度量AI 解读

General models of association between an angular and a linear variable, corresponding to monotone association between two linear variables, are proposed; U-statistics which are analogues of Kendall's tau are developed to measure such association, their distributions obtained, and their performances compared with other measures of angular-linear association.