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演化谱与非平稳过程AI 解读

Summary We develop an approach to the spectral analysis of non-stationary processes which is based on the concept of “evolutionary spectra”; that is, spectral functions which are time dependent, and have a physical interpretation as local energy distributions over frequency. It is shown that the notion of evolutionary spectra generalizes the usual definition of spectra for stationary processes, and that, under certain conditions, the evolutionary spectrum at each instant of…

非平稳时间序列中多项预测器与控制器的多项式投影性质AI 解读

Summary Box and Jenkins (1962, 1963) introduce a practical predictor for handling non-stationary types of time series and they show it to be optimal for a particular class of stochastic processes. As a consequence the predictor can be shown to follow stochastic as well as deterministic polynomial trends in the series. The present paper sets out to evaluate the bias term in the expression for the error when applying this predictor, and shows how the bias can be reduced…

投票定理在物理学与次序统计中的应用AI 解读

Summary The author finds the distribution of the number of gas molecules ionized by an electron passing through an electron tube, and the distribution of the deviation of empirical and theoretical distribution functions, when the sample size is a random variable having a Poisson distribution.

描述简单队列与水坝的随机游走的一项性质AI 解读

Summary A so-called duality principle, which has been given by previous authors for simple queues and dams, is here shown to be valid in more general circumstances. The conditions under which the result, relating the stationary distribution of one random walk with absorption probabilities in another, is applicable are investigated.

随机变量的关联与 Radon–Nikodym 导数的离散程度AI 解读

Summary In a previous paper by one of the authors (Silvey, 1964) it was suggested that the Radon–Nikodym derivative of the joint distribution of two, not necessarily real-valued, random variables with respect to the product of their marginal distributions provides the analytic key for discussing association between the random variables. In this paper we shall develop this point and lend some support to the suggestion by proving that in the case of normal random vectors the…

通过求解微分方程确定抽样分布与矩母函数AI 解读

Summary A method of obtaining sampling distributions and moment generating functions by solving differential equations is introduced. This method is demonstrated in finding the distribution of the difference of two gamma variates. A method closely related to the above is used in obtaining the moment generating functions of certain Pearson-type distributions.

超球面锥并集的概率界AI 解读

Summary In this paper are given two methods of obtaining bounds on the probability content of a union of hyperspherical cones in Euclidean N-space when the underlying distribution is normal. The results of a small numerical study are tabulated to indicate the range of applicability of the methods. These methods can be used to obtain bounds on the overall significance level and power-like probabilities in the analysis of variance when many treatment sums of squares are tested…

两个随机变量之比的方差恒等式AI 解读

Summary A new identity showing the relationship between the variance of the ratio of two random variables and the variance of the random variable in the numerator of the ratio is presented. For any sample design the identity offers a basis for exploring the conditions under which ratio estimators have smaller variance than linear estimators.

均一协方差情形下的估计AI 解读

Summary There are three basic methods (confidence, fiducial, Bayesian) of obtaining interval estimates or estimating regions for the parameters of the multivariate normal distribution, none of which need necessarily yield a unique solution, although this has been claimed as a property of the fiducial argument. It has been previously demonstrated that they are not consistent with one another, i.e. they yield different regions for the same parameters. In this paper we show…

置信区域检验AI 解读

Summary To test a hypothesis that a parameter has value θ* we usually ask whether an observation falls in a critical region of the outcome space. It is well known that, by a suitable choice of confidence region, an equivalent test is to ask whether θ* lies outside the confidence region. In this paper the concept of such a confidence-region test is extended in directions which are relevant to the study of data-snooping and multiple-hypothesis testing. These problems are…

一种二元符号秩检验AI 解读

Summary Wilcoxon (1945, 1947) proposed a signed rank test for the hypothesis of equality of means in samples of n matched pairs of observations from a bivariate population in (x, y). He stated the exact distribution of the sum (= U +) of the signed ranks of the positive differences z = x - y, as well as providing some tables of the significant values Uϵ+. The present paper gives a generalization of the Wilcoxon test using the sums of the signed ranks for two correlated or…

方差波动下的谱分析AI 解读

Summary The present paper is concerned with the following questions: (1) If a random sequence Xt (t = 0, ± 1, ± 2, …) is not second-order stationary, can one meaningfully define a spectral density function ? (2) If so, can one hope to consistently estimate it ? For the special case of a random sequence of form Xt=∑0pajσt−jηt−j, where the ηt are independently, normally, distributed with zero means and unit variances and the aj and σt-j are non-random finite quantities, it is…

一种两样本秩检验：Psi检验及其性质AI 解读

Summary Since the power of the Psi test proposed by Gibbons (1964) compares favourably with that of other one-sided, two-sample rank tests on the equality of two distribution functions, its properties merit further investigation. This paper is devoted to such a study. A table of exact critical values for the test statistic is given for selected small sample sizes, and compared with critical values for the approximate distribution which is a function of Student's t. The…

检验两个分布函数相等的两样本秩检验功效AI 解读

Summary This paper is a comparative study of the power functions of two-sample rank tests of the hypothesis of equal distributions, H 0: H = G. Numerical results are given for the alternative of two extreme distributions, H1:H=1−(1−F)k, G=Fk, with F an unspecified continuous cumulative distribution function, k = 2, 3, 4, sample sizes m = n ≤ 6, significance levels 0·01, 0·05, 0·10. Randomized decision rules are employed when necessary to attain the exact significance level.…

关于Wishart矩阵Bartlett分解的一则札记AI 解读

Summary By suitably factorizing the generalized variance, a concise derivation of the Bartlett decomposition of a central Wishart matrix is given. The method is extended to give a decomposition of a p-dimensional non-central Wishart matrix of rank t (≤ p), in terms of a t-dimensional non-central Wishart matrix of rank t, (p - t) independent χ2 variates and 1/2(p - t)(p + t - 1) independent unit normal variates.

响应相关时非线性回归区间估计的说明AI 解读

Summary Recent papers by Williams and Halperin discuss procedures for obtaining confidence regions† for parameters in non-linear regression. These results assume, among other things, independence and homoscedasticity of variance of the dependent variables. This note points out that by using some results of Rao it is possible to drop these latter assumptions.

Summary The application of idempotent matrices to the testing of linear hypotheses is discussed and several properties of idempotent matrices are given to simplify the calculation of the F-test statistic. It is also shown that the F-test is based on the so-called Wald principle of large sample theory and this approach is put forward as an alternative to the usual likelihood ratio method of deriving the F-statistic.

论局部推断与信息AI 解读

Summary Two techniques for local unbiased estimation have been developed in recent papers (Fraser, 1964a, b). In this paper these techniques are used to examine some aspects of inference and information. Both techniques show inadequacies for translation-invariant models, and this despite the development of the second technique on the basis of conditional sufficiency which is basic to translation-invariant models. Inference and information are then examined briefly for…

预测问题中贝叶斯与频率学派方法的比较：贝叶斯容忍域AI 解读

Summary In the theory of statistical tolerance regions, as usually presented in frequentist terms, there are inherent difficulties of formulation, development and interpretation. The present paper re-examines the basic problem from a Bayesian point of view and suggests that such an approach provides a set of widely applicable, mathematically tractable tools, often more tailored to the requirements of users than the corresponding frequentist tools. For the one-dimensional…

降雨发生的概率模型AI 解读

Summary A probability model for the occurrence of wet and dry days at Tel Aviv is proposed as an alternative to an earlier one given by Gabriel and Neumann. The new model, which assumes exponential distributions for the lengths of spells of continuous dryness or continuous rain, is found to fit rainfall data for Tel Aviv well, and to represent certain conditional probabilities more satisfactorily than that of Gabriel and Neumann.

多元回归的贝叶斯估计AI 解读

Summary In this paper, we use a Bayesian approach to analyse sets of regression equations with correlated error terms. In the case that the matrix of “independent variables” is the same for all equations, our model reduces to the traditional multivariate regression model. For this case, the marginal posterior distribution of the regression coefficient vector for any equation is shown to be of the multivariate-t form. Further, the variances and covariances of the error terms…

存在谐波分量时的谱密度函数估计AI 解读

Summary Consider a stationary process of the form Xt = Yt + Zt, where Yt is a linear process with a continuous spectrum, and Zt is a finite sum of harmonic components. We discuss two methods of estimating the spectral density function of Yt. In one method we first estimate the autocovariance function of Yt by “correcting” the sample autocovariance function of Xt, and then form the usual “smoothed” Fourier transform. In the other approach, we estimate the spectral density…

列联表交叉乘积比的同时置信限AI 解读

Summary Fisher (1962) has proposed a method for obtaining confidence limits for the cross-product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits for the cross-product ratio in a 2 × 2 table, and we shall extend these methods to obtain simultaneous confidence…

离散数据相关性估计的进一步模型AI 解读

Summary This note considers the distribution of the sum of n identically distributed multinomial variates Xi, the correlation coefficient for Xi and Xj being ρ for all i, j, i ≠ j. The initial model, with n and p' = (p1, p2,…,pk) fixed, is generalized by allowing first n, then p and finally both n and p to be random variables.