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分组数据下多元检验的渐近功效AI 解读

Summary In many situations (see, for example, Bennett, 1962), random variables which may be assumed to have a multivariate normal distribution cannot be measured exactly, but are each given one of a discrete number (usually two) of scores. One is therefore concerned with the problem of making inferences about the parameters of a multivariate normal distribution when the data are grouped. In this paper we consider the problem of testing the hypothesis that the mean vector is…

双正交归一展开在随机过程理论中的应用AI 解读

Summary Markov processes (with the exception of Gauss-Markov processes) are not in general Markov in the wide sense. Using a biorthonormal expansion of the second-order density function, it is shown that a class of Markov processes (not necessarily Gaussian) are Markov in the wide sense. These processes share some of the nice properties of Gaussian processes.

基于 n 排序法的渐近有效检验AI 解读

Summary The problem of finding asymptotically most powerful analysis of variance tests by the method of n rankings is studied here. In this context, characterizations of the optimality of the well-known tests by Friedman (1937) and Brown and Mood (1951) are also considered.

一般平衡设计中的信息合并AI 解读

Summary A general method is proposed for combining information in generally balanced designs when estimates of treatment effects are available from more than one stratum. Estimates of stratum variances are obtained by equating residual sum of squares in each stratum to their expectations, using the ML estimates of treatment effects. Weights may be given, the solution then being explicit, or fitted, in which case iteration is required. The results of a Monte Carlo study are…

残差的一般定义AI 解读

Summary Residuals are usually defined in connection with linear models. Here a more general definition is given and some asymptotic properties found. Some illustrative examples are discussed, including a regression problem involving exponentially distributed errors and some problems concerning Poisson and binomially distributed observations.

关于最小二乘估计效率的一则札记AI 解读

Summary A linear model is considered in which errors are independent and identically distributed with zero mean. If the error distribution is specified, except possibly for unknown parameters, the asymptotic efficiency of least-squares estimates relative to maximum-likelihood estimates can be found. For regression parameters orthogonal to the general mean the asymptotic efficiency, which is independent of the design matrix, is calculated explicitly for an Edgeworth series,…

贝叶斯推断的一种推广AI 解读

Summary Procedures of statistical inference are described which generalize Bayesian inference in specific ways. Probability is used in such a way that in general only bounds may be placed on the probabilities of given events, and probability systems of this kind are suggested both for sample information and for prior information. These systems are then combined using a specified rule. Illustrations are given for inferences about trinomial probabilities, and for inferences…

线性函数关系的贝叶斯估计AI 解读

Summary The purpose of this note is twofold. First, to demonstrate by means of an example that a statistical approach based solely on the likelihood function can be misleading, whereas the Bayesian method yields sensible results. Second, to develop the Bayesian method and apply the results to the problem of estimating a linear functional relationship. In Section 1 we discuss the likelihood approach. Section 2 concerns the Bayesian method, which is applied to the functional…

时间序列相关结构相容性检验的Quenouille扩展AI 解读

Summary Quenouille's test compares under stated assumptions the correlation structures of two lengths of time series to see if they are compatible. A test is here derived to compare any number of lengths of time series. As in Quenouille's test, the derivation depends on assumed or fitted values of autoregression coefficients; the test is shown to be insensitive to errors in these values.

与若干随机过程相关的一种分布AI 解读

Summary The distribution discussed is (a) the total number of games lost by the ruined gambler starting with a monetary units against an infinitely rich adversary in the classical ruin problem; (b) the total size of an epidemic in an infinite population starting with a cases and with constant probabilities of infection and recovery; (c) the number of customers served in a busy period (starting with a customers) of the queue M/M/1. These derivations, the relationships between…

利用零点估计平稳二元高斯过程的互谱AI 解读

Summary Under regularity conditions the cross-spectrum of a stationary, bivariate, Gaussian process, continuous in mean and with unit variance, may be estimated consistently as T → ∞ from the zeros in the interval [0, T] of its two components and the knowledge that the components have the same or opposite sign at time 0. The power spectra of the components may be estimated from the respective components' zeros alone. The estimates are asymptotically normal and unbiased.…

正态情形下二维两样本位置非参数检验的小样本功效AI 解读

Summary The exact power of a test U (Mardia, 1967) is obtained for normal location alternatives, but even for small samples the expression cannot be simplified. The empirical power function of the U-test is obtained and compared with the power of Hotelling's T2 by extending some efficiency measures and developing a new non-central T2 routine. It is found that the efficiency of the U-test relative to Hotelling's T2 test decreases with N and lies between 79 and 93 per cent.

Summary Two alternative methods for dealing with the problem of missing observations in regression analysis are investigated. One is to discard all incomplete observations and to apply the ordinary least-squares technique only to the complete observations. The alternative is to compute the covariances between all pairs of variables, each time using only the observations having values of both variables, and to apply these covariances in constructing the system of normal…

多元回归中的变量选择AI 解读

Summary This paper is concerned with the analysis of data from a multiple regression of a single variable, y, on a set of independent variables, x 1,x 2,...,xr. It is argued that the form of the analysis should depend on the use that is to be made of the regression, and that therefore an approach employing ideas from decision theory may be worth while. Two situations are analysed in this way: in the first it is desired to predict a future value of y; in the second we wish to…

非平稳过程的谱概念AI 解读

Summary Following a brief general description of the attitude adopted here to statistical models and definitions, a study of the problem of defining a spectrum for non-stationary processes is made. The approach is to determine first what one would wish to use such a spectrum for, and then attempt to discover whether this is possible. By the nature of the case no conclusive answer is possible, but the tentative conclusion drawn is that it is not.

摘要暂缺

非平稳过程的预测AI 解读

Summary We consider the problem of linear least-squares prediction for a class of non-stationary processes which possess “evolutionary spectral representations”. It is shown that, under certain conditions, such processes admit moving-average representations in terms of time-dependent coefficients. This feature enables us to develop a close analogue of the Wiener–Kolmogorov approach to the corresponding problem for stationary processes.

四字母词：环形排列中模式频数的分布AI 解读

Summary An alphabet of c letters is considered. There are, then, ck possible ordered sequences of k of these. Such k-sequences are grouped into λ mutually exclusive and exhaustive sets; members of each set (called k-patterns) are counted the same. A general expression for the joint generating function of the frequencies of occurrence of the different k-patterns is obtained when r letters, with fixed numbers of each sort, are randomly arranged in a ring. In particular,…

偏离指数分布的分析AI 解读

Summary A test for a Poisson process based on ordered sample values is proposed and its distribution and other properties derived. The test statistic is shown to be asymptotically normal and some further approximations to its distribution are investigated. The asymptotic relative efficiency of the test with respect to the asymptotically most powerful test against the alternative of gamma-distributed intervals is derived. Finally, a test for an incomplete sample is outlined.

似然原则与不变性原则AI 解读

Summary The likelihood and invariance principles, when combined, imply the probability principle, which allows only very restricted inferences about a parameter, based on an observation. It is suggested, in explanation, that the likelihood and invariance principles are valid under two different viewpoints of the model, and that these viewpoints are incompatible.

指数分布参数的估计AI 解读

Summary Some new estimators, which are unbiased with respect to some loss functions, are derived for the parameter in the exponential distribution. The corresponding Bayes estimators are also obtained. The comparison between these two kinds of estimation is discussed.

随机变量乘积的分布AI 解读

Summary The problem of finding the probability density function of the product of n identically distributed independent normal variables was solved by Springer and Thompson (1966). Their formulae for n ≤ 7 are simplified in this paper and generalized to an arbitrary number of factors. Similar formulae for the corresponding probability distribution functions are derived. The applicability of these results to the cases of the negative exponential, Weibull and gamma…

平均穿越率为无穷的一类高斯过程AI 解读

Summary A stationary Gaussian process X(t) is defined as locally Markov if the slope of its autocorrelation function has a finite jump at the origin. For such a process the mean rate of crossings at an arbitrary level a is infinite. For small (t2 − t1), the probability that X(t1) − a and X(t2) − a have opposite signs is calculated, both with and without the auxiliary condition, X(t3)∈ (x3, x3+dx3], …, X(tn+2)∈(xn+2, xn+2+dxn+2], where the times t3,…, tn+2 are all outside…

多项分布的贝叶斯显著性检验AI 解读

Summary A Bayesian significance test for multinomial distributions is discussed, together with the results of 18 numerical experiments in which the test is compared with non-Bayesian methods. Several different non-Bayesian criteria are considered because the circumstances under which their tail-area probabilities can be conveniently approximated differ from one to the other. A provisional empirical formula, connecting the Bayes factors with the tail-area probabilities, is…