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Summary In a review of tests based on spacings, Pyke (1965) constructs an empirical distribution function of uniform spacings, and suggests that goodness of fit problems could be investigated with Kolmogorov–Smirnov and Cramér–von Mises type statistics when applied to this empirical distribution function, were the appropriate exact or asymptotic critical values available. It is shown in this note that the limiting distributions of these statistics are indeed available, but…

关于无限可分点过程的一则札记AI 解读

Summary In the discussion of Cliff and Ord (1975), Westcott mentioned the problem of determining those point processes which are both doubly stochastic Poisson processes and Poisson cluster processes—the dual nature is of interest in model interpretation since the underlying mechanisms are radically different. This was related to the question of which doubly stochastic Poisson processes are infinitely divisible, and it was conjectured that this occurs if and only if the…

快速傅里叶变换谱估计量AI 解读

Summary This note shows how the Fast Fourier Transform (FFT) spectral estimator can be approximately written as an average of periodograms constructed at points 2πk/N removed, where k is an integer and N is the number of observations; it also shows the properties of this approximation.

密度及其导数估计在若干统计问题中的应用AI 解读

Summary Several statistical problems are considered. By reducing them to problems of estimating functionals of a density, derivatives of a density, or both, a method of finding partial solutions is obtained.

生态与疫情传播的空间接触模型AI 解读

Summary A wide variety of phenomena of geographical spread can be described in terms of a mechanism of “growth” (e.g. birth, infection) and a “contact distribution” which describes how the locations of the individual(s) involved in a migratory move, or infection at a distance, are spatially related. I shall survey work on such models, beginning with an examination of the relations between stochastic and deterministic models; it emerges that both linear and nonlinear…

交通流的排队模型AI 解读

Summary A model for queue formation and disintegration is proposed for traffic on a road where flow is unimpeded. The model assumes that vehicles are travelling in random queues and a distribution for queue length is derived having as a single parameter the ratio of the rate of mergings between pairs of queues and the rate of overtaking from queues of more than one vehicle. The first moment and maximum likelihood estimator associated with the distribution are derived and…

球对称矩阵分布与多元线性模型AI 解读

Summary We consider inference about the parameters of a multivariate linear model, in which the usual assumption of normality for the errors is replaced by a weaker assumption of spherical symmetry. Structural distributions and confidence regions are derived, and it is shown that inference about means is identical with that appropriate under normality, being based on a matrix generalization of “Studentization”. Some relevant distribution theory is developed, the approach…

回归函数的非参数估计AI 解读

Summary We consider a nonparametric technique proposed by Priestley and Chao (1972) for estimating an unknown regression function. Conditions for strong convergence and asymptotic normality are discussed. Special consideration is given to the optimal choice of a weighting function.

基于相关图大样本估计的季节性移动平均模型估计程序AI 解读

Summary In recent years considerable interest has centred on a family of moving average models proposed by Box and Jenkins (1970) for the description of time series which contain a seasonal component. A method is given in the paper for estimating the parameters of the seasonal models based on a principle due to Walker (1961) for the estimation of non-zero members of the autocorrelation function. An illustration of the method is given.

平稳双变量点过程中事件间隔的谱分析AI 解读

Summary A method is developed for analysing stationary bivariate point processes through their interval properties. The technique is based on representing the intervals as processes in continuous time. Expressions for a cross-covariance function and the corresponding cross-spectrum are given and some examples are considered. We note that use of this technique together with the device of smoothing makes computation of spectral estimates for point processes more efficient.

非正态变量二次型的分布及其在方差比中的应用AI 解读

Summary Good (1968a, b) using non-rigorous arguments, gave an expression for the characteristic function C.F. (x‘A x, t) of a quadratic form in a non-normal random column vector x whose characteristic function is known, where A is positive semi-definite. A general formula for C.F. (x‘A x, t) is proved here, which coincides with Good's expression when x has a real stable characteristic function. In the general formula, A need not be positive semi-definite and this greater…

论统计推断争议的解决AI 解读

Summary The controversy concerning the fundamental principles of statistics still remains unresolved. It is suggested that one key to resolving the conflict lies in recognizing that inferential probability derived from observational data is inherently noncoherent, in the sense that their inferential implications cannot be represented by a single probability distribution on the parameter space (except in the Objective Bayesian case). More precisely, for a parameter space R 1,…

作为估计捷径的F检验程序研究AI 解读

Summary When estimating fixed effects in the one-way anova model the F-test for the equality of the group means is sometimes used as a preliminary test of significance. This paper provides alternatives to the percentage points in the F-test by re-formulating the problem under estimation, as opposed to hypothesis testing, criteria. The new procedure possesses strikingly different properties, and it is argued that fixed-size tests are not obviously relevant within an…

二元平稳点过程二阶强度的估计AI 解读

Summary We consider histogram and smoothed histogram type estimates of the auto and cross intensity functions of a bivariate stationary point process. The asymptotic distributions are found to be multiples of Poissons in the histogram case and linear combinations of Poissons in the smoothed case. These asymptotic distributions suggest the plotting of the square roots of the estimates in order to stabilize the variance and to make the distributions more nearly normal. Two…

基于样本熵的正态性检验AI 解读

Summary A test of the composite hypothesis of normality is introduced. The test is based on the property of the normal distribution that its entropy exceeds that of any other distribution with a density that has the same variance. The test statistic is based on a class of estimators of entropy constructed here. The test is shown to be a consistent test of the null hypothesis for all alternatives without a singular continuous part. The power of the test is estimated against…

满指数族似然函数的因子分解AI 解读

Summary Examples are presented of full exponential families for which the likelihood function factorizes into a product of functions in such a way that each of the factor functions depends on a subparameter only and these subparameters vary independently of each other. A number of results are then discussed, concerning the key case of just two factors, one being the marginal likelihood for a statistic u, the other the conditional likelihood given u. Any statistic u which…

线性函数关系估计：近似分布及与计量联立方程的联系AI 解读

Summary When both variables are subject to error, a straight line may be fitted by minimizing the sum of squared distances of the observed points to the line. Approximate distributions of the slope of this line and of the angle it makes to one axis are given when the errors are normal, uncorrelated, and with equal variances. These distributions and corresponding ones for the line fitted by ordinary least squares are found by making the model equivalent to a model of…

矩阵加权平均与后验界AI 解读

Summary Bounds for matrix weighted averages of pairs of vectors are presented. The weight matrices are constrained to certain classes suggested by the Bayesian analysis of the linear regression model and the multivariate normal model. The bounds identify the region within which the posterior location vector must lie if the prior comes from a certain class of priors.

依赖观测下的最大似然估计AI 解读

Summary The asymptotic properties of m.l.e. are discussed for generally dependent observations. Conditions are derived for weak consistency and asymptotic Normality of the estimates. We further consider the case where some of the parameters are “transient” in the sense that the accumulated information on them from the sample does not increase indefinitely; then the interest lies in estimating the other parameters consistently. Examples are given, and the work is related to…

等信息析因设计的混杂矩阵与广义定义关系AI 解读

Summary In many practical situations a fraction of the full replicate of a k 1 x k 2 x ... x kt factorial is used by an experimenter to estimate a subset of effects under the assumption that the rest of the effects are negligible. to get a deeper insight in what precisely is being estimated if the assumption of negligibility of the suppressed effects is not valid it is imperative that the experimenter has a complete knowledge of the aliasing structure. This paper shows how…

缺失数据方差分析的非迭代最小二乘估计、标准误与 F 检验AI 解读

Summary This article generalizes Rubin's method of least squares estimation of missing values in an analysis of variance. The general method produces not only least squares estimates of all parameters and the residual mean square, but also the correct least squares standard error and t-test for each contrast as well as the least squares sum of squares and F-test for each collection of contrasts. The method is non-iterative and requires only those subroutines designed to…

载体传播流行病模型的参数估计AI 解读

Summary We derive the maximum likelihood estimates (m.l.e.) of the infection and removal rates of the carrier-borne epidemic model when the process has been observed continuously for a fixed or random period of time. For both sampling schemes we derive the distribution of the m.l.e. of the inverse of the removal rate. We also consider the problem of estimating the relative removal rate of the model when the process has been observed continuously for a period of time, but the…

利用删失数据构造均值的非参数置信区间AI 解读

Summary General Kolmogorov-type non-parametric confidence contours for an unknown continuous distribution function are converted into non-parametric confidence intervals for the mean of the distribution. It is shown how these estimation procedures may be modified to enable censored data to be handled.

任意分组、删失与截断数据的经验分布函数AI 解读

Summary This paper is concerned with the non-parametric estimation of a distribution function F, when the data are incomplete due to grouping, censoring and/or truncation. Using the idea of self-consistency, a simple algorithm is constructed and shown to converge monotonically to yield a maximum likelihood estimate of F. An application to hypothesis testing is indicated.