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协方差分析中的多重比较程序AI 解读

Currently available range-type procedures for constructing simultaneous confidence intervals on contrasts in analysis of covariance (ANCOVA) models with random covariates assume that the vectors of covariates associated with the observations are identically distributed. Conditions are given under which the mean vectors of these covariates may differ without affecting the validity of such procedures. An example of a controlled test market experiment illustrates the usefulness…

摘要暂缺

逆分布函数尾部的同时置信界AI 解读

Confidence bounds are derived for the upper 100$p$ percentile of an inverse distribution function. These bounds are considerably less conservative than similar bounds which apply to the entire function.

生长曲线技术在时间序列数据中的应用AI 解读

Techniques well established for the analysis of growth and dose response curves should provide useful tools for the analysis of time series data. After transforming the data to discrete Fourier transform coefficients, rather than to polynomial coefficients, as characterizes most growth curve techniques, further analysis is essentially the same. The circadian rhythm example reported by Ware and Bowden (1977) is reanalyzed, resulting in substantial reduction in width of…

生长曲线技术在时间序列数据中的应用AI 解读

Techniques well established for the analysis of growth and dose response curves should provide useful tools for the analysis of time series data. After transforming the data to discrete Fourier transform coefficients, rather than to polynomial coefficients, as characterizes most growth curve techniques, further analysis is essentially the same. The circadian rhythm example reported by Ware and Bowden (1977) is reanalyzed, resulting in substantial reduction in width of…

The actual percentage coverages attained in simultaneous confidence intervals on variance components with confidence level 1 –2α are investigated by Monte Carlo techniques. The results show that the percentage points l and u of the extreme roots of a Wishart matrix at α levels of 0·10 and 0·15 yield 0·95 and 0·90 confidence intervals, respectively.

非参数多重比较程序的前 k−1 组显著性水平AI 解读

We consider the nonparametric pairwise comparisons procedures derived from the Kruskal-Wallis $k$-sample test and from Friedman's test. For large samples the $(k - 1)$-mean significance level is determined, i.e., the probability of concluding incorrectly that some of the first $k - 1$ samples are unequal. We show that in general this probability may be larger than the simultaneous significance level $\alpha$. Even when the $k$th sample is a shift of the other $k - 1$ samples,…

Wishart矩阵极端特征根分位点应用的一则说明AI 解读

The actual percentage coverages attained in simultaneous confidence intervals on variance components with confidence level 1 –2α are investigated by Monte Carlo techniques. The results show that the percentage points l and u of the extreme roots of a Wishart matrix at α levels of 0·10 and 0·15 yield 0·95 and 0·90 confidence intervals, respectively.

处理组与对照组多重比较的部分序贯方法AI 解读

In this paper we propose a distribution-free treatments versus control multiple comparisons procedure, based on the control sample median, that is appropriate when the control sample observations are easy and relatively inexpensive to collect, while the treatments data are costly and/or difficult to obtain. For this procedure the control sample has a fixed sample size and the treatments have random sample sizes determined by a truncated inverse binomial sequential sampling…

删失数据下生存曲线的置信带AI 解读

For arbitrarily right-censored data, the Kaplan-Meier product-limit estimator Ŝ 0N provides a nonparametric estimate of the survival function S 0 = 1 − F 0 . We provide large-sample simultaneous confidence bands for S 0 , centred at Ŝ 0N . The derivation uses the weak convergence of N½ { Ŝ 0N ( t ) − S 0 ( t )}, on a finite interval, to a Gaussian process, a theorem of Breslow & Crowley (1974), and transforms both the time and space axes of the limiting process to achieve a…

简单线性模型百分位数曲线的紧置信带与容忍带AI 解读

This article develops sharp confidence bands for percentiles of regression functions over finite intervals. Attention is focused on one-sided (upper) bands for these percentiles, but a simple extension allows construction of two-sided bands. These upper bands are useful for tolerance bands, since a 100-γ percent confidence band for the 100/βth percentile is also a γ coefficient β-tolerance band.

非参数贝叶斯区间估计AI 解读

Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantilea and also for the mean. Bayesian tolerance limits are similarly constructed.

对数正态分布位置指标的置信估计AI 解读

Based on a random sample from the N(ξ, σ1) distribution, we find confidence bands with level 1 − α for exp(ξ +bσ1) for all 6. The method is based on a technique discussed by Kanofeky (1968a, b). Using the likelihood ratio confidence region for (ξ, σ1) (Spjøtvoll, 1972) as starting point we find that the probability that the confidence interval for a particular value of b covers the true value is fairly constant under variation of b, σ and the sample size. This makes it…

构造给定类中全部最小同时置信集及其MANOVA应用AI 解读

A method is presented for the construction of all families of smallest simultaneous confidence sets (SCS) in a given class, for a family $\{\psi_i(\gamma)\}$ of parametric functions of the parameter of interest $\gamma = \gamma(\theta)$. The method is applied to the MANOVA problem (in its canonical form) of inference about $M = EX$, where $X$ is $q \times p$ and has rows that are independently multivariate normal with common covariance matrix $\Sigma$. Let $S$ be the usual…

Kaplan–Meier 生存曲线估计的置信带AI 解读

The weak convergence of the Kaplan-Meier estimate for censored survival data to a Gaussian process is used to construct asymptotic confidence bands for the survival curves. The method involves transforming to obtain Brownian motion and using straight line boundaries and hitting probabilities for Brownian motion.

摘要暂缺

线性模型置信带的精确性AI 解读

Let S denote a confidence band for a linear model obtained by taking the envelope of a size 1 — α convex confidence region about the parameters. It is known that the degree of confidence associated with S is, in general, greater than 1 — α. Folks and Antle gave a sufficient condition on the model for the confidence band to be of size 1 — α. The necessity of Folks and Antle's conditions is proven here for the class of closed and convex regions with a smooth boundary. A…

非参数多重比较程序AI 解读

A general nonparametric methodology for performing multiple comparisons of treatment effects in r-way mixed models is presented. Comparisons can be made among all treatments or for several treatments against a control. The methods can be used on either the raw data or ranked data. Essentially, we perform M permutations of the observations, consistent with our experimental design. For the comparison of all treatments, any “treatment differences” that are larger than 95…

非参数贝叶斯区间估计AI 解读

SUMMARY Bayesian confidence bands for a distribution function are converted into confidence intervals for specified population quantiles and also for the mean. Bayesian tolerance limits are similarly constructed.

对数正态分布位置指标的置信估计AI 解读

Based on a random sample from the N(ξ, σ1) distribution, we find confidence bands with level 1 − α for exp(ξ +bσ1) for all 6. The method is based on a technique discussed by Kanofeky (1968a, b). Using the likelihood ratio confidence region for (ξ, σ1) (Spjøtvoll, 1972) as starting point we find that the probability that the confidence interval for a particular value of b covers the true value is fairly constant under variation of b, σ and the sample size. This makes it…

不平衡设计中多重比较 T 方法扩展的改进AI 解读

Some improvements and clarifications of extended T-type procedures of multiple comparisons for unbalanced designs are given. In view of the general discussion, we obtain a procedure particularly tailored for one-way layouts with only two different sample sizes. In all such designs, the given procedure yields confidence intervals which are not longer than those obtained by Spjøtvoll and Stoline's (1973) method for all pairwise comparisons and are strictly shorter for some of…

分布函数的贝叶斯置信带AI 解读

A set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known. When the prior parameter is unknown and is estimated from the sample, nonparametric estimates of the probability content of the posterior bands are obtained.

Wishart 矩阵特征根的正相依性AI 解读

It is shown that the characteristic roots of a Wishart matrix (identity covariance matrix) and the roots of $S_1 S_2^{-1}$ and $S_1(S_1 + S_2)^{-1}$ where $S_1, S_2$ are independent $p \times p$ Wishart matrices with the same covariance matrix, satisfy certain types of dependency relationships. That is, it is shown that these roots are (a) positive orthant dependent, (b) associated, (c) stochastically increasing in sequence, and (d) positively likelihood ratio dependent. An…

单变量与多变量 Behrens–Fisher 型问题的同时置信程序AI 解读

Given independent samples of size ni from normal populations with mean μi and variance σi2 both unknown, it is possible to construct simultaneous confidence intervals for all linear combinations of μi's with an exact predetermined confidence coefficient by using the tabulated values of Student's t distribution and a generalization of the maximum modulus method of multiple comparisons. These bounds are shown to be a special case of a class of exact bounds based on a variant…