日期精度：到日 2575 篇 · 到月 3 篇 · 到年 0 篇
系统性振荡检验的修订
Summary This note suggests a revised test for the existence of systematic oscillation in the deviations of a time series from a fitted moving average. It is shown that the existing test may be misleading and simple alternative formulae are derived, though the test still remains subjective in the sense that the sampling distributions involved have not yet been derived.
正态变量二次型的迹与累积量
Summary The cumulants of a quadratic form in n independent standardized variables are identified with the traces of the powers of the matrix of the form. This identification leads to some very simple proofs of well-known theorems. It is proved that only in a normal system is it possible to have non-trivial linear transformations from one set of independent variables to another set of independent variables. Matrix proofs are given for the Cochran theorems paying special…
农业调查中的样本配置与估计问题
Summary A sampling method which has been used in fertilizer surveys in England and Wales is described. The relative efficiencies and biases of several methods of estimating average fertilizer dressings are determined from the results of eight surveys carried out in 1950. The unbiased method of estimation is found to be 65 per cent efficient relative to the unweighted mean of the field observations; this latter method is only slightly biased. An alternative method of…
马尔可夫自回归过程参数的置信区间
Summary An investigation is made of two suggested methods by which confidence intervals might be indirectly obtained for the autocorrelation in a stationary first-order Markov series. The suggestions were to use in the one case the distribution of the mean of the disturbance terms, and in the other case the distribution of their serial correlation. It is shown that both methods give meaningful results if the observations do not diverge too greatly from the characteristics of…
各种卡方近似的乘数因子札记
Summary A list is given, for reference, of various approximate tests, based on the asymptotic approximations for likelihood ratios, but with adjusted multiplying factors.
格子抽样的误差
Summary Lattice samples are samples selected from a multiple classification of units with one unit in each subclass in such a way that they include equal numbers of units from each main class or from each combination of two, three or more main classes in different classifications. The present paper provides a discussion of the errors of such samples. Methods for determining the sampling variances from the complete data, when these are available, for purposes such as a…
基于破纪录次数的时间序列分布无关检验
Summary Two simple statistics are proposed as distribution-free tests of the randomness of a series of observations. They are linear functions of the numbers of upper and lower records which occur in the series. They are uncorrelated and asymptotically normally distributed. One provides a consistent test against trend in the mean and the other a consistent test against trend in the variance. Power functions for the former test have been computed, and it is pointed out that…
不等概率抽样理论的若干结果
Summary The main purpose of the present paper is to give a rule for calculating estimates of sampling error which can be applied to multi-stage designs of any degree of complexity. The rule is an extension of that given by Yates (1949) for the case of equal probabilities of selection. The paper goes on to discuss the relation between the theories of sampling with and without replacement and two approximate procedures are described which are easy to apply but lead to slight…
分层内按规模比例进行不放回抽样
Summary In selection with probability proportional to size x from within strata without replacement, the usual method of selection gives rise to bias in the estimate of the total of a variate y derived by weighting the units by weights proportional to 1/x. By means of numerical examples it is shown that the amount of this bias is usually quite trivial. If, however, unbiased estimates are required, the true total probabilities of selection of the different units can be…
Wilcoxon两样本检验的功效
Summary Pitman’s formula for the variance of a distribution-free test of two samples, due to Wilcoxon, is evaluated for some special cases. The upper bound of this variance is derived, and a population is constructed in which this upper bound is attained. The value of the variance is then used to find the power of the test against normal and rectangular alternatives for large samples and to compare this test with certain distributional tests.
生灭过程参数的估计
Summary In a previous paper the estimation of the sum λ + μ of the parameters of a simple birth and death process was considered. In the present paper we consider the estimation of λ(λ + μ)−1. This problem is equivalent to the problem of estimating the probabilities of steps to the right and left from an observed realization of a random walk which has one absorbing boundary and which is terminated, if necessary, after a preassigned number of steps. The properties of various…
多变量自回归序列的拟合优度检验
Summary The simplified method of derivation of Quenouille’s (1947) goodness of fit test for an autoregressive stationary series with discrete time, given by Bartlett and Diananda (1950), is extended in the present paper to the case of simultaneous autoregressive series, for which some interesting new features arise. The general solution is applied to a particular first-order process in two variables, the detailed correlational theory of which is being given elsewhere by…
随机过程理论在不可重复化学反应与成核过程研究中的应用
Summary The irreproducibility of some chemical reactions is due either to (A) the inherent mechanism of the process or (B) extraneous factors (e.g., impurities). The purpose of this paper is to show that mathematical techniques developed in recent years permit the quantitative calculation of statistical properties of reactions of the type (A). An exposition of some general methods is given; their application to some typical chain mechanisms shows that conditions for the…
统计推断
Summary The subject matter of mathematical statistics may be divided into two parts, the theory of probability and the theory of inference. The first is concerned with deductions from the population to the sample; the second with inferences from the sample to the population, and may further be subdivided into the design and analysis of experiments. In the present paper we are concerned with this latter subdivision. We use the axiomatic theory of Kolmogorov as our theory of…
多元平稳时间序列分析
Summary After some preparatory work, the least square estimation equations are derived for a purely nondeterministic stationary multiple process (Th. 6). The asymptotic covariances of the parameter estimates are calculated for a normal process (Th. 9) and a test of fit derived (Th. 10). The testing of a sunspot model provides an illustration of the methods developed.
序贯估计
Summary The literature on sequential estimation is reviewed, with special reference to inverse binomial sampling, double sampling, and asymptotic theory. An approximate distribution for the sample size is found for a certain type of sequential sampling rule, in which a cumulative sum of independent random variables all having the same continuous distribution is plotted against their number until a fixed boundary is first reached or crossed. Approximate methods are given for…
离散分布序贯抽样数据的参数估计
Summary It is supposed that a constant finite discrete population (which may have arisen through grouping another population) is sampled, with replacement, until some linear function of the frequencies reaches a predetermined value. The generating function of the final frequencies is found exactly when each coefficient in the linear function is either 0 or +1, and the asymptotic means, variances and covariances in more general cases by using an extension of Wald’s identity.…
系数随时间趋势变化的二阶自回归模型
Summary It has been suggested that the departure of certain time series from a fitted second order autoregressive scheme is due to time-trending coefficients in the generating differential equation. If coefficients with linear time-trends are introduced into the scheme the correlogram of the resulting non-stationary series can, in special cases, be evaluated exactly in terms of Airy integrals and is found to be approximately of the form sin s/s where s is proportional to the…
人体测量学的若干统计问题
Summary This paper deals with some statistical problems arising in the treatment of anthropometric data on a large scale. its aim is not so much to develop new statistical methods as to apply critically well known techniques. The first part of the paper discusses the problem of collecting and recording the data in a way that will minimize the number of gross errors and will be well adapted to the subsequent computing processes. The rest of the paper exhibits three typical…
线性自回归模型拟合优度检验的渐近功效函数性质
Summary Quenouille (1947), and Bartlett and Diananda (1950), have given large sample goodness-of-fit tests of the hypothesis that a time series can be represented by a linear autoregressive scheme with independent residuals. Asymptotic power functions of these tests are derived for alternative hypotheses specified by linear autoregressive schemes of higher order with independent residuals, and of the same or higher order with residuals among which there exists dependence of…
二项总体中较小类别比例的置信区间
Summary Given a random sample from an infinitely large population consisting of two kinds of individuals, in unknown proportions, a confidence interval is determined for the smaller of these proportions. A numerical example is given, and an application is suggested.
表示正常细菌生长的数学模型选择
Summary The problem considered is that of constructing a stochastic process (not necessarily of the Markov type) to represent the growth of a bacterial colony in the absence of mortality and mutation. The importance of the distribution of fission-times is emphasized, and an approximate relation between the coefficient of variation of the fission-times and the asymptotic coefficient of variation of clone-size is discussed. Rahn’s model of the fission process, a rather…
受突变影响的细菌种群统计理论
Summary This paper is a study of the growth of a mixed bacterial population composed of two types of organisms, and subject to mutation from one type to the other, in one or both directions. The bacteria divide by binary fission, but the rates of division for the two types may differ. The paper is intended as a unified and critical presentation of statistical results previously published by other authors, together with a number of new results. The first part presents a…
统计分析中的主观判断：一项实验研究
Summary As part of an experimental study of the effect of stopping iterative maximum likelihood calculations after one cycle, twenty-one scientists were asked to judge by eye the positions for a pair of parallel probit regression lines in a biological assay. This paper reports the results obtained from each pair of lines after one cycle of various forms of probit calculation. Although all the conditions of the experiment were chosen so as to be unfavourable to the drawing of…