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一类具有特定结构的矩阵的行列式、特征方程及其根的计算AI 解读

SUMMARY The variance–covariance matrices arising in the analysis of variance, response-surface fitting and order statistics have special patterns expediting and facilitating their algebraic manipulation. By appropriate triangulation and partitioning devices, the determinants of these matrices can be evaluated from general formulae. The characteristic equations, and sometimes their roots, can also be obtained in a direct single step.

适于计算机实现的多元数据缺失值估计方法AI 解读

SUMMARY Estimation of statistical parameters from multivariate data results in wasted information, if units with incomplete data are rejected entirely, and perhaps in inconsistencies in the variance–covariance matrix if the variances and correlation coefficients are estimated from all available data on individual variates and pairs of variates respectively. An alternative is to estimate the missing values by regression techniques and to calculate a revised…

Summary In estimating the regression coefficient of y on x, we can sometimes increase precision by using supplementary observations, u. We need to have prior information about the form of the relations among y, x, and u. An implication for experimental design is noted.

最大似然估计程序及其配套显著性检验AI 解读

Summary The essence of many statistical problems, including most standard techniques, is to test whether or not the unknown parameters of an appropriate statistical model satisfy certain restrictions; and the outcome of such a test dictates whether it is necessary to provide estimates of these parameters which also satisfy the restrictions. In this paper we discuss and illustrate the relative merits, as practical tools for the consulting statistician, of two large-sample…

时间序列回归模型的参数估计AI 解读

Summary We consider the estimation of the coefficients in a general linear regression model in which some of the explanatory variables are lagged values of the dependent variable. For discussing optimum properties the concept of best unbiased linear estimating equations is developed. It is shown that when the errors are normally distributed the method of least squares leads to optimum estimates. The properties of the least-squares estimates are shown to be the same…

经典回归与双重抽样估计的理论AI 解读

Summary This paper examines the various classical results in the theory of regression and double sampling estimation and extends them to the study of a finite population.

利用 Pistimetric 概率预测自回归过程的说明AI 解读

Summary The distributions of the parameters and of the future values of a Markov scheme are obtained by a technique which combines the use of Bayes' theorem with the method of inference sometimes considered appropriate to situations where there exist sufficient estimators.

从若干正态总体中选择最大均值AI 解读

Summary Consider a k-variate normal distribution with unknown means μ 1, …, μk and with equal variances and equal covariances whose values are known; the problem is to select the variate associated with μ max using a single-sample procedure of size n, and, in particular, to determine the required value of n. Previous work is reviewed. New results are given assuming that the population means μ 1, …, μk have a joint a priori normal distribution with means U 1, …, Uk known up…

非线性估计中的置信区域AI 解读

Summary The statistical properties of the approximate confidence regions for nonlinear estimation based on the likelihood ratio criterion are considered, assuming normal variation of errors. It is suggested that these approximate confidence regions are preferable to any known exact confidence regions for this problem, provided that the model is only moderately non-linear. A numerical measure of the non-linearity of a model (as a function of the experimental design and the…

计量检验中最经济的序贯抽样方案AI 解读

Summary The two-point prior distribution of Barnard (1954) is used and leads to a method for calculating most economical sampling schemes for variables. An example is worked out where observations on items are normally distributed, and an application is given to determining most economical sampling schemes for group sequential sampling for attributes.

固定巡检间隔下自动络筒机的效率AI 解读

Summary The problem is that of maximizing the average efficiency of a machine which (i) stops when its total running time has reached a fixed value a, (ii) has accidental stops, and (iii) is patrolled for servicing (i.e. re-starting if necessary) at a fixed interval p which may be less than a, efficiency being defined as the ratio of the running time to the total time under consideration. The probability distribution of the number of patrols required to exhaust the total…

基于删失样本的均匀总体位置与尺度参数估计AI 解读

Summary Best linear estimates of location and scale parameters under conditions of Type II censoring are obtained for the rectangular distribution. In addition, functions of the location and scale parameters such as the start and end of the distribution, as well as percentile points, are also estimable. A special case occurs where the rectangular distribution starts at the origin. Tables are available from the authors to furnish coefficients to facilitate all computations…

控制图与随机过程AI 解读

Summary A new approach to control charts for industrial processes is suggested, based on the idea that the underlying stochastic process should be specified, its parameters estimated, and the control procedure related to these. Optimum estimators are derived, and practical approximations to these are indicated.

Summary Hotelling's test of significance for difference in efficiency of predictors is reformulated in terms of regression analysis. A test proposed by Healy is shown to differ from Hotelling’s test in general.

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随机区组实验中的删失观测AI 解读

SUMMARY Maximum likelihood methods are developed for the analysis of data from randomized block experiments, when some of the observations are censored. A modification of the maximum likelihood process, intended to produce approximately unbiased estimates of variance, is described, and the results of some numerical investigations into its efficacy are reported. Analogues of the t-test, using two alternative formulae for standard errors of differences, are considered, with…

两总体选择问题中的另一种损失函数AI 解读

SUMMARY In previous discussions of the problem of balancing sampling costs against the cost of choosing the wrong population it has been assumed that the cost of sampling is equal to the sample size multiplied by a constant known unit cost. In the present paper the cost of sampling is assumed to be the cost of an incorrect choice for half of the sample programme (which is divided evenly between the two populations). The resulting loss function is considered when the choice…

统计谱分析中的带宽与分辨能力AI 解读

SUMMARY The purpose of this paper is to refute Grenander’s latest objections to the authors' work on statistical spectral analysis, and to clarify the distinction between resolvability, bandwidth, and bias.

余料的统计理论AI 解读

SUMMARY In certain manufacturing processes where varying lengths of material are produced and subsequently cut up into unit lengths the problem of loss from wasted material arises. In this paper we postulate a statistical model of such a process and study how and in what sense we may minimize this loss. Two simple tests of whether a process is under optimum control are proposed. Finally we consider briefly two extensions of the theory to corresponding problems in k…

若干依赖累计停留时长的随机过程AI 解读

SUMMARY The problem considered is that of two discrete states in continuous time; the transition probabilities depend on the total time, t, spent in, say, state 1. The probability that at a given time τ the process is in state i and the total time spent in state 1 lies in (t, t + δt) is derived. Some limiting cases for which the transition probabilities are powers of t are considered. The probability that the total time spent in state 1 reaches t in the interval (τ τ+ δτ) is…

相关且非齐性误差下多因素方差分析中各平方和的分布AI 解读

SUMMARY The distributions of various sums of squares in an analysis of variance table for two-way classification have been obtained by Box (1954b), under the assumption that the row-vectors X.j(j = 1, 2, …, q) are independent vector observations from a p-variate normal population, where X.j consists of those p observations which correspond to the p levels of a factor A, for the j th level of another factor B. This paper gives the distributions of the various sums of squares…

机器服务干扰的若干问题AI 解读

SUMMARY The problem of interference arises when a team of operatives is attending a set of machines, these being assumed to have a certain servicing factor. In this paper an estimator of the servicing factor and a simple expression for the machine efficiency are introduced. A loss function is also given, with a method for the determination of an appropriate number of operatives to be applied for the attendance of the machines.

用工具变量估计残差自相关的关系AI 解读

SUMMARY The instrumental variables method of estimating the coefficients of a linear relationship between time series which have measurement errors is applied to the case where the coefficients are functions of a set of parameters. The asymptotic error variance matrix of the estimates is obtained, asymptotic tests for the existence and identification of the suggested form of relationship are suggested, and asymptotic confidence regions are given. The general theory is then…