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摘要暂缺

一般线性模型中百分位数线的同时置信带AI 解读

This article is a generalization of the procedures developed by Steinhorst and Bowden (1971) for constructing confidence bands for the 100βth percentiles in the general linear model. Since the original procedure built these bands about a biased estimator of the 100βth precentile line, some other estimators were tried. While some improvement was noted, the results are not conclusive, suggesting that the best procedure has not been found yet.

对称性的图形诊断与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…

K 样本线性秩统计量两种排序方法的渐近等价性AI 解读

Two methods of ranking $K$ samples for rank tests comparing $K$ populations are considered. The first method ranks the $K$ samples jointly; the second ranks the $K$ samples pairwise. These procedures were first suggested by Dunn (1964), and Steel (1960), respectively. It is shown that both ranking procedures are asymptotically equivalent for rank-sum tests satisfying certain nonrestrictive conditions. The problem is formulated in terms of multiple comparisons, but is…

若干变分结果及其在多重推断中的应用AI 解读

Let $(\mathbf{M}, \mathbf{T}, \mathbf{S})$ be random matrices such that $\mathbf{M}$ and $\mathbf{S}$ are Hermitian positive definite almost everywhere. Let $\mathbf{M}_{(t)} = \lbrack m_{ij}; 1 \leqq i, j \leqq t\rbrack, \mathbf{S}_{(t)} = \lbrack s_{ij}; 1 \leqq i, j \leqq t\rbrack$ and $\mathbf{T}_{(r,s)} = \lbrack t_{ij}; 1 \leqq i \leqq r, 1 \leqq j \leqq s\rbrack$, and define $Q(r, s) = P\lbrack G((\mathbf{M}_{(r)})^{-\frac{1}{2}}\mathbf{T}_{(r,s)}(\mathbf{S}_{(s)}) ^{-\frac{1}{2}}) \leqq c\rbrack$…

介于 Tukey 与 Scheffé 方法之间的同时推断程序AI 解读

Two well-known simultaneous inference procedures for balanced one-way layout are Tukey's T-method and Scheffé's S-method. The T-method gives short simultaneous confidence intervals for all pair-wise comparisons while paying a high price for high-order comparisons. The S-method is appropriate when one has uniform interest in all contrasts, but gives long confidence intervals for pairwise and other low-order comparisons. In this paper we propose a family of procedures…

介于 Tukey 与 Scheffé 方法之间的同时推断程序AI 解读

Two well-known simultaneous inference procedures for balanced one-way layout are Tukey's T-method and Scheffé's S-method. The T-method gives short simultaneous confidence intervals for all pair-wise comparisons while paying a high price for high-order comparisons. The S-method is appropriate when one has uniform interest in all contrasts, but gives long confidence intervals for pairwise and other low-order comparisons. In this paper we propose a family of procedures…

论统计推断争议的解决AI 解读

Summary The controversy concerning the fundamental principles of statistics still remains unresolved. It is suggested that one key to resolving the conflict lies in recognizing that inferential probability derived from observational data is inherently noncoherent, in the sense that their inferential implications cannot be represented by a single probability distribution on the parameter space (except in the Objective Bayesian case). More precisely, for a parameter space R 1,…

分布对称性的图示与检验AI 解读

We consider plots which can be used to check whether a distribution is symmetric about some point and which give information about possible deviations from symmetry. Simultaneous confidence bands for checking the accuracy of the plots are derived and compared. Tests that are related to the plots and confidence bands are considered and their power functions are compared using Monte Carlo methods. As tests of normality, the powers of two of these tests compare favourably with…

β的最小比例方差线性无偏估计量与同时置信区间AI 解读

Pr [tfi E ,i 4i ta/k(n-k)avii fori = 1, 2, ... k] > 1-a (6) since tjk (n k) < I kFa (k, n k) . The set of t-intervals (6) constitute a confidence cuboid for g at an unknown significance level. In this paper we establish a confidence cuboid for I at a known significance level which may be superior to (6) as Ma (k, f) < talk (f). This confidence cuboid is based on the minimum proportional-variance unbiased linear estimator of g which has a mean square error matrix that exceeds…

摘要暂缺

成对与多项比较模型的对数线性表示AI 解读

This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the ø coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex data seta…

摘要暂缺

非标准随机区组设计中精度不等的多重比较AI 解读

A multiple comparison technique for simultaneous inference in the nonstandard randomized block design models considered by Graybill [3] and Scheffé [11] is developed. Its computation and properties are discussed in terms of a clinical trial. The technique involving a number of independent tests with possibly unequal sizes, not the well-known Bonferroni tests [5], is appropriate when most contrasts between the treatments are of interest, but a few of the comparisons are of…

平衡不完全区组模型参数的同时置信区间AI 解读

Inferences concerning the variance ratios of a random linear model are important in genetics and other areas of scientific investigation. For example, in genetics, the heritability parameters are functions of the variance ratios of a random model. This paper derives simultaneous confidence intervals for all or certain subsets of the parameters of a balanced incomplete random model. This procedure is based on the mean squares of the analysis of variance, and the mean squares…

正态总体分位数的置信带AI 解读

Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic,…

非标准随机区组设计中精度不等的多重比较AI 解读

A multiple comparison technique for simultaneous inference in the nonstandard randomized block design models considered by Graybill [3] and Scheffé [11] is developed. Its computation and properties are discussed in terms of a clinical trial. The technique involving a number of independent tests with possibly unequal sizes, not the well-known Bonferroni tests [5], is appropriate when most contrasts between the treatments are of interest, but a few of the comparisons are of…

正态总体分位数的置信带AI 解读

Given the general linear regression model , where y is N X 1, X of full rank is N X (q + 1), is (q + 1) X 1, and e is N(0, σ2I), Steinhorst and Bowden [5], using the theory of Roy's maximum root test statistics, set confidence bands for , of the normal population with mean and variance σ2, k being the pth quantile of the standard normal distribution, I fixed or specified but unknown and p known. However, narrower bands may be obtained using the exact test statistic,…

方差不等的单因素设计中 T 多重比较法的修正AI 解读

Tukey's T-method for simultaneous inference in a one-way layout is extended to situations where heterogeneity of variance prevails. The modified method is based on the distribution of the range of iid Student-t variates. The new procedure is exemplified and a table of critical values is provided for its implementation. A different procedure based on a Bonferroni upper bound is also discussed.

将 Tukey 多重比较方法扩展至具有随机伴随变量的实验设计AI 解读

SUMMARY A procedure is provided for the construction, of simultaneous confidence intervals on all contrasts of a set of parametric functions, or tests of hypotheses concerning them, in an analysis of covariance wherein the dependent and concomitant variates have a joint (p + 1)dimensional normal distribution. This new procedure is analogous to Tukey's method of multiple comparisons in the analysis of variance, both in application and in the conditions which are necessary for…

成对比较与多项比较模型的对数线性表示AI 解读

SUMAIARY This paper develops log linear model representations for the Bradley-Terry paired comparisons and Luce multiple comparisons models. Various multivariate extensions of the Bradley-Terry model are then considered. A model is presented, similar to one of Davidson & Bradley (1969), but which is based on the log odds ratio as a measure of association rather than the 0 coefficient of correlation. It is shown that, by the adaptive use of log linear model theory, complex…

带截距回归曲面的单侧同时置信界AI 解读

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffé two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

含截距回归曲面的单侧同时置信界AI 解读

Exact one-sided simultaneous confidence bounds are obtained for general regression surfaces with intercepts and functionally independent regressors. For all values of the regressors, the distance from the regression surface to the one-sided bound is a fixed fraction (less than one) of the corresponding distance to the well-known Working-Hotelling-Scheffé two-sided bound. Tables are provided to facilitate the use of such one-sided bounds.

多设计多元线性模型下一般线性假设的检验AI 解读

The generalization of the standard model for MANOVA which allows for the possibility of different "design" matrices for the variates is known as the multiple design multi variate linear model. For example, in multivariate regression analysis we might have polynomial models of different degree in the "independent" variates. In this paper, new tests are given for the general linear hypothesis under the multiple design multivariate model and in one case the corresponding…