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区间上简单线性回归的精确置信带AI 解读

Exact simultaneous confidence intervals and bands for the regression line on a set Cx in simple linear regression have been known only when Cx is a finite set with one or two points or when Cx is a finite or infinite interval. Otherwise, conservative bands have been used. In this article we present a method for constructing exact confidence bands on an arbitrary finite union of intervals or points. Also, tables are provided for cases of finite Cx with three points and of Cx…

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

面向使用者的统计推断AI 解读

A class of inferential procedures (called user-oriented procedures) related to the equal probability test of Arrow (1960) is introduced for use in many univariate problems. These procedures require that experimenters be able to interpret the parameters about which they wish to make inference. The class of procedures include confidence intervals associated with the equal probability test as well as an analogue to the P value. The confidence intervals are easier to interpret…

一般多元方差分析模型中的同时区间估计AI 解读

Let $M \in M(m, p)$ be the matrix of means of interest in the GMANOVA problem. Our main results characterize all confidence sets for $M$ in a given class (invariant plus a weak additional restriction) that are exact for the families of parametric functions $a'Mb$ for all $a \in \mathbb{R}^m, b \in \mathbb{R}^p$ and $\operatorname{tr} N'M$ for all $N \in M(m, p)$. The corresponding families of smallest exact simultaneous confidence intervals are also given. Similar results…

Hunter 同时推断方法及其在高相关已知结构中的应用AI 解读

The Hunter (H) method of simultaneous estimation of all means is based on a second-order Bonferroni-type inequality and is superior to the Bonferroni (B) method. This method is applicable for cases using a multivariate t distribution with correlation matrix R = (ρ ij ) and is shown to be decidedly superior to the B method when the correlations ρ ij in R are all large (|ρij| > .5). This article presents an example, using data from Draper and Smith (1966), in which the 95…

Hunter同时推断方法及其在已知高相关结构中的应用AI 解读

The Hunter (H) method of simultaneous estimation of all means is based on a second-order Bonferroni-type inequality and is superior to the Bonferroni (B) method. This method is applicable for cases using a multivariate t distribution with correlation matrix R = (ρ ij ) and is shown to be decidedly superior to the B method when the correlations ρ ij in R are all large (|ρij| > .5). This article presents an example, using data from Draper and Smith (1966), in which the 95…

乘积极限估计量在整条实线上的大样本性质AI 解读

Weak convergence results are proved for the product-limit estimator on the whole line. Applications are given to confidence band construction, estimation of mean lifetime, and to the theory of $q$-functions. The results are obtained using stochastic calculus and in probability linear bounds for empirical processes.

针对非嵌套备择模型的精确检验AI 解读

The results of Milliken & Graybill (1970) are used to develop a general procedure for obtaining exact tests of a linear model against several nonnested and nonlinear alternatives simultaneously. The procedure may be extended to test a null model against alternatives in which the dependent variable is subjected to different data transformations. Arguments are presented in favour of multiple tests.

区组设计中相对于最佳处理的同时推断AI 解读

In many practical situations, only inference concerning the unknown best treatment and comparisons of the individual treatments with respect to the best treatment are of primary interest. We give an explicit formulation of this problem in the framework of randomized complete block designs. A procedure based on sample means and two procedures based on signed ranks are proposed. It is seen that, for the problem considered, these procedures have a substantial advantage over…

构造同时置信区间的一般方法AI 解读

A general method is proposed for constructing simultaneous confidence intervals that gives special emphasis to any preselected finite spanning subset in a linear space of estimable functions. The method has a wide range of application, including regression analysis. The length of a confidence interval is determined as the solution to a linear programming problem. The studentized maximum modulus distribution can be used to choose critical values for conservative control of…

具有多元随机效应协方差结构的多元重复测量与增长曲线模型AI 解读

The analysis of multiple-response, repeated-measurement or growth curve models with a multivariate random-effects covariance structure for individuals is considered. Results on estimation, hypothesis testing, and simultaneous confidence bounds for the parameters of the generalized linear model of Potthoff and Roy (1964) are derived for the multiple-response repeated-measurements model under the multivariate random-effects covariance structure. Two numerical examples are…

正态均值比的同时置信区间AI 解读

Given one or more groups of multivariate normal samples, methods are presented for forming simultaneous confidence intervals of all ratios of linear forms of the mean vectors. The methods cover the cases of equal or unequal covariances. In a simultaneous inference context, they are multivariate extensions of a method due to Fieller (1954) for estimation of the ratio of two normal means.

随机完全区组设计中处理差异的渐近分布无关同时置信域AI 解读

Summary For a randomized complete block design with additive block effects, an asymptotically distribution-free simultaneous confidence region of pairwise treatment differences is presented. The corresponding confidence bound has an explicit form and is easily obtained. Asymptotic relative efficiency comparisons with other known confidence regions are made to show the advantage of the proposed procedure. The case of treatment against control is also discussed.

对称分布的非参数估计AI 解读

Substantial improvements in the accuracy of nonparametric estimates are achieved when the centre of a symmetric distribution is known. Resultant benefits for confidence bands for the distribution function are extended to confidence intervals for quantiles and also tolerance limits. When the symmetry centre is not known and must be estimated from the sample improvements in accuracy are still possible.

随机模型中方差分量函数的同时置信区间AI 解读

Interval estimation of certain functions of variance components is of interest to research workers in all fields of applications in which the variance component model is used. Confidence intervals for linear functions and ratios of variance components have been proposed by several authors. For the most part, these intervals are approximate with unknown exact probabilities associated with their coverage. In this article a technique is given for the construction of…

所有对象相对“最优者”差距的同时置信区间AI 解读

In practice, comparisons with the "best" are often the ones of primary interest. In this paper, parametric and nonparametric simultaneous upper confidence intervals for all distances from the "best" are derived under the location model. Their improvement upon the results of Bechhofer (1954), Gupta (1956, 1965), Fabian (1962), and Desu (1970) in the parametric case is discussed. In the nonparametric case, no comparable confidence statements were available previously.

学生化极差检验的一种多元对应形式AI 解读

It is well known that T max 2 test procedure, a multivariate analog of studentized range test, can be derived by using Roy's union intersection principle with a bilinear decomposition of the MANOVA hypothesis that is response-wise infinite and contrastwise finite. In this article an alternative union intersection derivation of T max 2 test is presented using the matrix decomposition of the MAN-OVA hypothesis. This decomposition is responsewise as well as contrastwise…

学生化极差检验的一个多元对应形式AI 解读

It is well known that T max 2 test procedure, a multivariate analog of studentized range test, can be derived by using Roy's union intersection principle with a bilinear decomposition of the MANOVA hypothesis that is response-wise infinite and contrastwise finite. In this article an alternative union intersection derivation of T max 2 test is presented using the matrix decomposition of the MAN-OVA hypothesis. This decomposition is responsewise as well as contrastwise…

基于朴素估计量的失效率函数大样本估计与一致置信带AI 解读

In this paper we consider a naive estimator of the failure rate function and smooth it using any band-limited window. We show that this smoothed estimate is equivalent to estimates obtainable from the sample hazard function, as in Rice and Rosenblatt (1976). We obtain the asymptotic distribution of the global deviation of the smoothed estimate from the failure rate function, which can then be used to construct uniform confidence bands.

随机删失数据的拟合优度图与检验AI 解读

In this paper, we consider nonparametric procedures for assessing goodness of fit when the data may be subject to random censoring. We introduce two classes of large-sample tests, based, respectively, on the maximum and average weighted difference between the specified survival function and the Kaplan-Meier estimate of the true survival function. The procedures in the first class are inverted to obtain simultaneous confidence bands for the survival and cumulative hazard…

随机删失的 Koziol–Green 模型AI 解读

In the Koziol–Green (1976) model of random censorship the survival distribution of the censoring variables is some power, the censoring parameter, of the survival distribution of the lifetimes. Using a strong approximation result of Burke, Csörgó and Horv´th, we construct empirical exact confidence bands for the life distribution of the censored variable, and a randomly Efron-transformed variant of the usual product-limit process is shown to converge weakly to the Brownian…

随机删失数据的拟合优度图与检验AI 解读

In this paper, we consider nonparametric procedures for assessing goodness of fit when the data may be subject to random censoring. We introduce two classes of large-sample tests, based, respectively, on the maximum and average weighted difference between the specified survival function and the Kaplan-Meier estimate of the true survival function. The procedures in the first class are inverted to obtain simultaneous confidence bands for the survival and cumulative hazard…

预测变量范围受限时的线性回归置信带AI 解读

The classic procedure for constructing a confidence band around a regression function is that of Scheffé (1959), which provides a band of infinite length. This band can be unnecessarily wide if the region of interest to the experimenter is finite. A class of sets is defined that restricts the range of the predictor variables. Confidence bands for a regression function over are constructed, which, for fixed α, are narrower than the Scheffé bands. Also, a procedure is…

普通线性模型与复相关模型中 F 检验的渐近有效性AI 解读

In this article we establish under fairly general conditions that the F tests used in the linear model and the correlation model are asymptotically valid in the presence of nonnormality, in that their sizes are unaffected, asymptotically, by this nonnormality. Similar results could be derived for Scheffé-type simultaneous confidence intervals as well as the one-sided t tests used in these models. Finally, we find the asymptotic distribution of the sample variance and show…