日期精度：到日 2575 篇 · 到月 3 篇 · 到年 0 篇
未知方差正态总体均值的序贯置信区间
Summary A modified sequential procedure is put forward for the problem of estimating the mean of a normal population by a confidence interval of prescribed width and confidence coefficient, when the population variance is unknown. Certain problems akin to the latter are discussed and wherever possible comparison is made with some results of Anscombe based on his asymptotic theory.
适用于截断数据的两类位置变化检验比较
Summary The powers of one and two-sample tests of change of centre of location based on the difference of sample quantiles are compared with those of the corresponding combinatorial tests based on quantile division of the sample. The powers are found to be asymptotically equivalent. Computation of particular cases suggests that for quite small samples there is good agreement of the powers of the two kinds of test with each other and with their common limiting form.
曲线与周期图平滑
Summary The difficulty in constructing smoothing formulae is to express quantitatively the type of smoothness one expects of the curve one is estimating. An argument is given in Sections 1 and 3 for formulating this “smoothness hypothesis” in terms of the properties of a population of curves of which the curve being estimated is a member. In equation (20) we obtain a solution for the matrix of optimum weighting coefficients in terms of certain “population moments” of the…
随机过程谱密度函数的估计
Summary On the basis of an expected-mean-square-error criterion, the authors discuss the various hitherto proposed estimators of the spectral density function of a discrete-parameter process; they also introduce a new estimator. Any of these estimators depends on some parameter, and indications are given as to how this parameter should match those of the process in order to optimize the estimator. The alleged conflict between resolvability and statistical reliability is…
时间序列的谱分析
Summary (i) A review has been made of spectral analysis and its relation with other branches of time-series analysis. A detailed account has been given of the methods available for estimating the spectral density, the band spectrum and the integrated spectrum; suggestions have also been made for confidence intervals for the latter two estimators. (ii) Emphasis has been laid throughout upon the difficulties which are met in practice and gaps in the theoretical structure have…
Summary The main results in both the discrete and continuous cases are summarized side by side in Tables 8 a and 8 b .
批量服务队列中的极限分布
Summary The limiting behaviour is discussed of a simple queueing process, in which customers. arrive at random, form a single queue in order of arrival, and are served in batches, the size of each batch having a fixed maximum, as this maximum tends to infinity. Limiting distributions are obtained for the situations where the service interval has a χ2 distribution with an even number of degrees of freedom, and the queue is assumed to be in equilibrium. These situations…
单个变量观测不完整时的多元离散分析
Summary In analysis of dispersion (multivariate generalization of the analysis of variance) Wilks' A criterion for testing hypotheses on all the multiple characters simultaneously cannot be applied if some observations on one or more of the characters are missing. In this article is provided a suitable criterion when data become incomplete due to missing observations in one of the characters only. This is the likelihood ratio criterion with a slight modification. The exact…
自相关时间序列之间关系的回归分析
Summary The properties of complete systems of linear regression equations, (in particular systems of the closed-loop and recursive type) are discussed in Part I, while least-square estimators and estimators of the Gauss-Markoff type are examined in Part II.
基于复相关系数的若干检验的渐近功效
Summary Pitman (1948) has proposed a criterion of the relative power of two tests of an hypothesis specified by a single parameter, based on the estimating efficiencies of the two test statistics, in case these test statistics are asymptotically normal. This criterion can be immediately generalized to many cases where the two statistics have limiting distributions of the same analytical form and, in particular, enables two tests based on statistics which are asymptotically…
切比雪夫不等式的推广
Summary We may often obtain the lower moments of a sampling distribution when the distribution itself is intractable. Tchebycheff’s celebrated inequalities for the cumulative distribution function are of very little use in practice, being “much too wide”. The present work obtains generalizations of these inequalities by restricting the distribution function to be “smooth” in two senses: firstly, by restricting the number of changes of sign of some derivative, and secondly by…
列联表中小频数的估计
Summary Suppose that we require estimates of the population frequencies corresponding to small entries in a large pure contingency table containing heterogeneity. It would be natural to lump rows or columns together with weights depending on the correlation coefficients. But if the rows, say, are nearly orthogonal, no lumping method will be reasonable. Moreover, if many of the entries in the table are missing, a lumping method may fail. A method is given here (which it may…
正态多元系统维数显著性检验计算程序的代数理论
Summary Before attempting to allot individuals to one of a set of normal multivariate populations, it is usual to make preliminary tests of significance to discover the structural relationships of the populations. In order to secure this reduction there are two separate methods, due to Fisher and (essentially) to Wilks. A simple algebraic proof is given for the identity of the statistics obtained from the two methods, and the condition under which Fisher’s method leads to…
按长度排序的随机区间若干注记
Summary The joint probability distribution of several magnitudinally ordered intervals of a line is derived together with a moment generating function belonging to it. Some limiting distributions are given and the rate of convergence is examined. The distributions of some simple functions such as the ratio and difference of two ordered intervals are derived.
有限总体抽样的统一理论
Summary The most general type of linear estimate is defined for a general sampling design. It is demonstrated that an unbiased linear estimate with least variance does not exist uniquely for the entire class of linear estimates. A slightly modified criterion for best estimate, with reference to certain given prior information is proposed. Some sampling designs have been analysed accordingly.
马尔可夫链的若干分布与矩公式
Summary An exact formula (8) is derived for the probability distribution of an observed set of transition totals. This expression furnishes asymptotic expressions for the likelihood (24), for the covariances of transition totals (27), and for the distribution of Bartlett’s goodness-of-fit statistic (31). Formulae are also derived for the expectations of some sample functions related to the factorial moments of the transition totals (34) and for the lower moments of the…
与事件序列有关的若干统计方法
Summary The paper deals with a number of problems of statistical analysis connected with events occurring haphazardly in space or time. The topics discussed include: tests of randomness, components of variance, the correlation between events of different types, and a modification of the snap-round method used in operational research.
负阶矩与比率统计量
Summary A simple method is considered of obtaining the moments of the sampling distribution of a ratio, when the numerator and denominator are independent.
Summary A description of an experiment (see title) carried out on an automatic computer.
去趋势马尔可夫序列最小二乘回归的数值研究
Summary The variation in the standard error of the regression coefficient between two trend-reduced time series, constructed from Markoff series, is examined for various choices of the trend-reducing operator. Tables are given to facilitate computation, for the regression between trend-reduced time series which approximate to Markoff series in their local variational properties.
去趋势时间序列的最小二乘回归分析
Summary The difficulties of obtaining a valid estimate of the standard error of a regression coefficient between two time series are discussed. It is shown how a preliminary trend-reducing operation on the series, using a moving average, makes it possible to obtain such a valid estimate. A method of analysis is described, along with considerations which affect the best choice of moving average for the purpose, which is applicable when the local variational properties of the…
支持范围依赖参数且存在充分统计量时的参数置信区间
Summary This paper gives the sampling distribution of a sufficient statistic (which is also the maximum likelihood statistic) for the parameter of a distribution when the range of the distribution depends upon the parameter. Confidence intervals for the parameter are obtained, based on the distribution of the sufficient statistic.
统计方法与科学归纳
Summary The attempt to reinterpret the common tests of significance used in scientific research as though they constituted some kind of acceptance procedure and led to “decisions” in Wald’s sense, originated in several misapprehensions and has led, apparently, to several more. The three phrases examined here, with a view to elucidating the fallacies they embody, are: (i)“Repeated sampling from the same population”,(ii)Errors of the “second kind”,(iii)“Inductive behaviour”.…