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线性判别函数的矩与对数优势比的渐近置信区间AI 解读

A general expression is obtained for the moments of a statistic which contains Anderson's linear discriminant function and the minimum variance unbiased estimator of the log odds ratio as special cases. The result is given in terms of certain invariant polynomials of matrix argument, and is used to derive the first four exact central moments, together with asymptotic expansions of the cumulants. This provides an alternative approach to Okamoto's expansion as an Edgeworth…

线性判别函数的矩与对数优势比的渐近置信区间AI 解读

A general expression is obtained for the moments of a statistic which contains Anderson's linear discriminant function and the minimum variance unbiased estimator of the log odds ratio as special cases. The result is given in terms of certain invariant polynomials of matrix argument, and is used to derive the first four exact central moments, together with asymptotic expansions of the cumulants. This provides an alternative approach to Okamoto's expansion as an Edgeworth…

矩阵变量不变多项式及其在计量分布理论中的应用综述AI 解读

Invariant polynomials with matrix arguments have been defined by the theory of group representations, generalizing the zonal polynomials. They have developed as a useful tool to evaluate certain integrals arising in multivariate distribution theory, which were expanded as power series in terms of the invariant polynomials. Some interest in the polynomials has been shown by people working in the field of econometric theory. In this paper, we shall survey the properties of the…

适度多元非正态性对 Roy 最大根检验的影响AI 解读

The asymptotic distribution of Roy's largest root statistic in multivariate Edgeworth populations is expanded to terms of the first order. To this order, the effects of non-normality are expressed by Mardia's measures of multivariate skewness and kurtosis, together with a supplementary skewness measure. Tables of corrections to the nominal significance level are presented for the k-sample MANOVA situation. Comparison with simulation results indicates that the correction…

适度多元非正态性对Wilks似然比准则的影响AI 解读

A technique for the formal construction of statistical distributions in multivariate Edgeworth populations is applied to investigate the effects of moderate multivariate nonnormality on the test statistics used in connexion with the general linear model, in particular, Wilks's likelihood ratio criterion. The first-order approximation to the sampling distributions under nonnormality are shown to involve Mardia's measures of multivariate skewness and kurtosis, together with a…

适度多元非正态性对威尔克斯似然比准则的影响AI 解读

A technique for the formal construction of statistical distributions in multivariate Edgeworth populations is applied to investigate the effects of moderate multivariate nonnormality on the test statistics used in connexion with the general linear model, in particular, Wilks's likelihood ratio criterion. The first-order approximation to the sampling distributions under nonnormality are shown to involve Mardia's measures of multivariate skewness and kurtosis, together with a…

摘要暂缺

Meijer 函数的微分方程与 Wilks 似然比准则的补充分位数表AI 解读

The null distributions of a number of likelihood ratio criteria are well known to be expressible in terms of Meijer's function. It is shown that such distributions correspond to a single fundamental solution of the differential equation for this function at the regular singularity one. Computation of percentage points of Wilks's likelihood ratio criterion by analytic continuation of this solution fills some gaps in the previously published tables.

单变量与多变量 Edgeworth 总体中的统计量分布AI 解读

A general method is presented for the formal construction of statistical distributions in univariate and multivariate populations, when the underlying distributions are specifiable by Edgeworth-type expansions. It is shown that the distribution of a statistic may be derived in principle from the appropriate normal-theory noncentral distribution, by means of a symbolic expectation operator. This provides a unified approach to the results of numerous investigations into the…

单变量与多变量 Edgeworth 总体中的统计量分布AI 解读

A general method is presented for the formal construction of statistical distributions in univariate and multivariate populations, when the underlying distributions are specifiable by Edgeworth-type expansions. It is shown that the distribution of a statistic may be derived in principle from the appropriate normal-theory noncentral distribution, by means of a symbolic expectation operator. This provides a unified approach to the results of numerous investigations into the…

一类似然比准则的百分位数近似AI 解读

The general asymptotic series developed by Box (1949) for the distributions of a large class of likelihood ratio criteria has been widely used to obtain good approximations to these distributions. A direct percentile approximation based upon this expansion, bearing a relationship to it similar to that of the Cornish-Fisher expansion to Edgeworth's series is given.

一类似然比检验准则的百分位数近似AI 解读

The general asymptotic series developed by Box (1949) for the distributions of a large class of likelihood ratio criteria has been widely used to obtain good approximations to these distributions. A direct percentile approximation based upon this expansion, bearing a relationship to it similar to that of the Cornish-Fisher expansion to Edgeworth's series is given.

Hotelling 广义 T20 统计量的精确分布AI 解读

Percentile tables are given for the null distribution of Hotelling's generalized T20 statistic. These are obtained by analytic continuation of Constantine's series using a system of linear differential equations. The accuracy of certain approximations given by Pillai and Ito is discussed.