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协方差分析中的多重极差检验AI 解读

A new test statistic is proposed for making multiple comparisons on adjusted treatment means in analysis of covariance when the dependent and concomitant variates have a multivariate normal distribution. The probability distribution of the range of the adjusted treatment means, suitably Studentized, is derived for the case of one-way analysis of covariance with equal subgroup sizes and one random covariate, and the distribution is found to be free of nuisance parameters.…

两样本非线性模型的经验概率图与统计推断AI 解读

Let $X$ and $Y$ be two random variables with continuous distribution functions $F$ and $G$ and means $\mu$ and $\xi$. In a linear model, the crucial property of the contrast $\Delta = \xi - \mu$ is that $X + \Delta =_\mathscr{L} Y$, where $= _\mathscr{L}$ denotes equality in law. When the linear model does not hold, there is no real number $\Delta$ such that $X + \Delta = _\mathscr{L} Y$. However, it is shown that if parameters are allowed to be function valued, there is…

协方差分析中的多重极差检验AI 解读

A new test statistic is proposed for making multiple comparisons on adjusted treatment means in analysis of covariance when the dependent and concomitant variates have a multivariate normal distribution. The probability distribution of the range of the adjusted treatment means, suitably Studentized, is derived for the case of one-way analysis of covariance with equal subgroup sizes and one random covariate, and the distribution is found to be free of nuisance parameters.…

连续对称分布的拟合优度检验AI 解读

This article considers the problem of testing a completely specified continuous symmetric distribution against alternatives which are also symmetric about the same point. The symmetry is utilized in obtaining a new distribution-free statistic of the Kolomogorov-Smirnov type which can be used to halve the width of the Kolomogorov-Smirnov confidence band for the unknown distribution function.

用于构造置信带的随机变量的极限分布AI 解读

The limiting distribution of the random variable, √n times the maximum absolute difference between Φ(x;x,s) and Φ(x;0, 1) is obtained, where Φ(x;μ,σ) denotes the normal cumulative distribution with mean μ and variance σ2 and x and s2 are, respectively, the mean and variance of a random sample of size n from Φ(x;0, 1).

摘要暂缺

纤维束强度的固定宽度置信带AI 解读

The present paper deals with the asymptotic theory of sequential confidence intervals of prescribed width $2d (d > 0)$ and prescribed coverage probability $1 - \alpha (0 < \alpha < 1)$ for the (unknown, per unit) strength of bundle of parallel filaments. In this context, certain useful convergence results on the empirical distribution and on the bundle strength of filaments are established and incorporated in the proofs of the main theorems. The results are the sequential…

乘积型交互对比的同时置信区间AI 解读

Summary The set of product-type interaction contrasts, which contains the subsets of interaction residuals, tetrad contrasts, double-dichotomy contrasts and pooled-tetrad contrasts, is discussed. In the Normal case with equal and known variances, simultaneous confidence intervals for a given set of such contrasts can be constructed in several ways. Five such methods (the Scheffé method, the Tukey method, the Dunn method, a method based on Roy's maximum-root statistic and a…

置信带构造中一个随机变量的极限分布AI 解读

The limiting distribution of the random variable, √n times the maximum absolute difference between Φ(x;x,s) and Φ(x;0, 1) is obtained, where Φ(x;μ,σ) denotes the normal cumulative distribution with mean μ and variance σ2 and x and s2 are, respectively, the mean and variance of a random sample of size n from Φ(x;0, 1).

逆线性回归中的同时置信区间AI 解读

Suppose that we are concerned with estimates of the parameters in a linear regression model and with a large number of observations of the dependent variable. Different observations may correspond to different values of the independent variable. The problem of finding simultaneous confidence intervals for the values of the independent variable is considered. Asymptotically the probability of the event, that at least a prescribed proportion p of the intervals contains the…

摘要暂缺

累积分布函数参数置信带的一种构造方法AI 解读

A method is developed for constructing a confidence band for a cumulative distribution function with known functional form. The band is derived using the maximum absolute difference between the true function and an estimator of it. The normal distribution with unknown mean and variance is treated in detail. The band derived in this case is found to be superior in certain instances to the one due to Kanofsky (1968a) with respect to the expected band width at selected points,…

百分位数的同时置信带与判别集合AI 解读

Using the general linear model, y = Xβ+e, where e∼N(0, σ2/): simultaneous confidence bonds are found for the 100 pth percentile, x′β+kpσ, of the normal population with mean x′β and variance σ2 (kp is the 100 pth percentile of the standard normal distribution). The bands are simultaneous in x or in x and p. In the simple linear regression case these bands are used to define simultaneous discrimination sets for any fixed values, yP, of the dependent variable.

判别与百分位数置信带AI 解读

Using the general linear model, y = Xβ+e, where e∼N(0, σ2/): simultaneous confidence bonds are found for the 100 pth percentile, x′β+kpσ, of the normal population with mean x′β and variance σ2 (kp is the 100 pth percentile of the standard normal distribution). The bands are simultaneous in x or in x and p. In the simple linear regression case these bands are used to define simultaneous discrimination sets for any fixed values, yP, of the dependent variable.

回归分析中的同时置信带AI 解读

Summary Simultaneous confidence intervals for linear combinations of parameters in a regression analysis are discussed, and a desirable property is described. Confidence intervals having this property are characterized and the Working–Hotelling band is discussed with reference to it. It is shown how this band may be sharpened to give exact confidence levels in linear and quadratic regression. Tables are given from which the confidence bands may be constructed.

多个 Student t 变量最大绝对值的分位点表及应用AI 解读

A table of lOOγ% points of the maximum absolute valuetof the k-variate Student t distribution with v degrees of freedom and common correlation p is given for various values of k, ν, p and γ. The application of these tables to problems dealing with the construction of simultaneous confidence and prediction intervals is briefly described.

线性回归模型的同时置信带AI 解读

In this article a procedure is given for constructing confidence bands of various forms for linear regression models. Application of the procedure yields, as special cases, hyperbolic, straight line segment, uniform width and trapezoidal confidence bands.

等概率检验及其在若干同时推断问题中的应用AI 解读

Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations…

等概率检验及其在若干同时推断问题中的应用AI 解读

Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations…

This paper is concerned with the use of spectral analysis to analyze data generated by computer simulation experiments with models of economic systems. An example model serves to illustrate two different applications of spectral analysis. First, spectral analysis is used to construct confidence bands and to test hypotheses for the purpose of comparing the results of the use of two or more alternative economic policies. Second, spectral analysis is employed as a technique for…

一类二元卡方分布的不等式AI 解读

The inequality is shown to hold when the joint distribution of U 1 and U 2 is a member of a class of bivariate Chi-Square distributions given. The relevance of this result to the construction of two-sided simultaneous confidence intervals for variances is noted.

方差的同时置信区间AI 解读

Given a sample of n vector observations from a multivariate normal population, Anderson and Roy-Gnanadesikan have given for the variances a set of confidence intervals which are approximate in that a lower bound only is known for the joint confidence coefficient. In the present study, exact procedures are developed in terms of multivariate Chi-Square distributions, and more general approximate procedures are given via Bonferroni's inequality. A numerical investigation…

Wishart 矩阵极端特征根的分位点AI 解读

This paper tabulates the distribution of the largest and smallest characteristic roots of a Wishart matrix; the computation is based on an approximation derived from work of Pillai. As an application, we present simultaneous confidence intervals for the variance components of the two-way layout with unequal variance.

有限区间内回归直线置信带的一则说明AI 解读

In a recent article Graybill and Bowden give a method for constructing a confidence band for the entire regression line in simple linear regression. Each bound consists of two straight line segments rather than of the usual branch of a hyperbola. The method uses tables of the studentized maximum modulus with parameter m = 2 and d.f. = n − 2.The present note suggests a method for obtaining linear confidence bands designed to be used over a finite range rather than from − ∞ to…