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有限总体抽样中的主观贝叶斯模型AI 解读

Summary A general and basic model for inference about characteristics of a finite population of distinguishable elements is presented from a subjectivistic–Bayesian point of view. A subjectivist analogue to simple random sampling, based on the notion of exchangeable random variables, is discussed and the inputs and assumptions underlying the model are shown to involve nothing more than is required for inference under Bayesian models for infinite populations. The model is…

Summary The effects on the distribution of least-squares residuals of a series of model mis-specifications are considered. It is shown that for a variety of specification errors the distributions of the least-squares residuals are normal, but with non-zero means. An alternative predictor of the disturbance vector is used in developing four procedures for testing for the presence of specification error. The specification errors considered are omitted variables, incorrect…

卷积分布的参数估计AI 解读

Summary Parametric estimation problems are considered when one observes a random variable which is the sum of two independent non-identically distributed random variables. Some basic identifiability theorems are given which suggest the method of moments as a general method for attacking such problems, particularly when one of the summand variables is discrete. Moment estimators and their asymptotic distributions are examined for various specific examples. Some applications…

非平稳信号的滤波AI 解读

Summary We observe a record consisting of a “signal” plus “noise” up to the time instant t, and wish to extract the value of the signal at the time instant (t + m) by means of a linear filter. Here, m may be positive (corresponding to “prediction”) or negative (corresponding to “smoothing”). In this paper we consider the case where both the signal and noise processes are non-stationary and possess evolutionary spectral representations. Using this approach we obtain a close…

时间序列非平稳性的检验AI 解读

Summary We consider the problem of testing a given time-series for stationarity. The approach is based on evolutionary spectral analysis, and the proposed method consists essentially in testing the “homogeneity” of a set of evolutionary spectra evaluated at different instants of time. Using a logarithmic transformation, we show that the mechanics of the test are formally equivalent to a two-factor analysis of variance procedure when the residual variance is known, a priori.…

预测变量为比例时的回归问题AI 解读

Summary That proportions must sum to unity results in the need for adaptations to commonly used regression techniques when these are applied to proportions. Some such adaptations are considered here.

Summary Cox and Snell have introduced a definition of residuals, in a situation more general than the usual linear hypothesis. They have also discussed briefly the distribution of these residuals, and the complementary aspect of transforming them so that they have (approximately) the same distribution as the random variables which they are effectively estimating. Here it is shown how a complete discussion can be given.

双变量两样本非参数检验的零假设分布AI 解读

Summary A non-parametric test criterion U for the bivariate two-sample problem has been proposed by Mardia (1967). It is shown in Mardia (1968) that a two-sample test on a circle proposed by Wheeler and Watson (1964) has the same null distribution as that of U. In view of this additional application, we extend the table of critical values of U given in Mardia (1967), give a new approximation to the null distribution and compare it with the approximations given in Mardia…

后验分布的渐近行为AI 解读

Summary Let a random sample of size n be taken from a distribution having a density depending on a real parameter θ, and let θ have an absolutely continuous prior distribution with density π(θ). We give a rigorous proof that, under suitable regularity conditions, the posterior distribution of θ will, when n tends to infinity, be asymptotically normal with mean equal to the maximum-likelihood estimator and variance equal to the reciprocal of the second derivative of the…

非负、单调或凸约束下的多项式最小二乘拟合AI 解读

Summary An algorithm is provided to fit the (unique) least-squares polynomial Y(x) to n data points (x, y) subject to a constraint that it be either non-negative, non-positive, non-decreasing, non-increasing, convex or concave at all points x in a closed interval I. Some generalization to a general linear model can be handled, and certain alternative constraints can also be dealt with. The problem is close to the classical problem of Quadratic Programming (Q.P.), and some of…

最小二乘理论的基础AI 解读

Summary The Bayesian theory of least squares is founded upon a weaker and more tangible form of prior knowledge than the conventional assumption of normality. The underlying assumption is a form of conditional uniformity on spheres for the “actual errors” in the experiment. This provides a unified theory appropriate for randomization models in the analysis of variance as well as for classical least-squares analysis.

多元正态分布的中心容忍区域AI 解读

Summary In a multivariate normal distribution the probability density takes any particular value at all points on the surface of an ellipsoid whose centre is the mean of the distribution. Among such ellipsoids there is one, R, say, that contains 100α per cent of the individuals in the population. The paper deals with the problem of determining from a random sample a region which contains R with prescribed probability β. In the univariate case, R reduces to an interval with…

点过程的叠加AI 解读

Summary Given point processes N1, …, Nm their superposition is the point process N defined by N(t) = N1(t) + … + Nm(t), t ≥ 0. An equivalent description of the system (N1, …, Nm) is by the process (Xn, Tn) where the Tn are the points of N, and Xn = k if and only if Tn is a point of Nk. The use of (X, T) process enables one to study the dependence of N1, …, Nm. Necessary and sufficient conditions are obtained for N, …, Nm to be independent, and for the superposition N to be a…

样本分位数渐近分布的一则说明AI 解读

Summary This paper gives a rigorous proof, under conditions believed to be minimal, of the asymptotic normality of a finite set of quantiles of a random sample from an absolutely continuous distribution. The proof is substantially simpler than those that have previously been published.

精确πPS抽样方案：Hanurav方法的推广AI 解读

Summary In his recent paper Hanurav (1967) discussed the problem of optimum utilization of auxiliary information for the estimation of the total (or mean) of a finite population and gave some solutions to the problem for the case of samples of size 2. In this paper we extend one of his procedures (sampling scheme A“ in his paper) to cover general sample sizes and also prove some of its optimum properties. The method is illustrated on the data given in Hanurav's paper.

有限总体抽样中的分布无关充分性AI 解读

Summary The concept of distribution-free sufficiency, (DF-sufficiency for short) for estimation in survey sampling, which has been introduced by Godambe (1966), is investigated. Uncorrelatedness in Godambe's definition is shown to be equivalent to statistical independence, as is claimed on the author's behalf in the appendix to Godambe's paper. But the second result claimed there, that every DF-sufficient estimate must necessarily be of the form a(s).∑i∈sxi+b(s) is false, as…

随机排列AI 解读

Summary The problem of generating random permutations of the integers 1, 2, …, n arises, for example, when sampling a randomization distribution and when tables of permutations are required for application to experimental design. An algorithm is described which minimizes the amount of randomization necessary to generate a random permutation, although in practice longer but simpler procedures are likely to be preferable. We discuss the probability distributions for the number…

多元 Beta 分布与多元正态性检验AI 解读

Summary This paper presents an application of the multivariate beta distribution to the problem of testing whether a given sample of multivariate observations could have come from a multivariate normal population with an unknown mean vector and dispersion matrix. By using a series of transformations and the principle of randomization it is shown that the above problem can be reduced to that of testing for univariate normality. No attempt is made to investigate the power of…

次可加随机过程的遍历理论AI 解读

Summary An ergodic theory is developed for the subadditive processes introduced by Hammersley and Welsh (1965) in their study of percolation theory. This is a complete generalization of the classical law of large numbers for stationary sequences.

向量时间序列中最小二乘估计的效率AI 解读

Summary A theorem due to Rosenblatt (1959) concerning the circumstances under which least squares is asymptotically efficient for the estimation of the matrix of regression parameters in a system of regressions is re-formulated in a simpler form and is extended. A theorem is proved relating to the efficiency of least squares under linear constraints which is not specifically of a time series nature.

有限混合分布的参数估计AI 解读

Summary This paper is concerned with the estimation of the parameters of a finite mixture of distributions. The components of the mixture are assumed to belong to a subset of the exponential family of distributions. A procedure for estimation has been developed and the resulting estimators are shown to be consistent and asymptotically normally distributed. Finally, as applications, mixtures of two binomial and two exponential distributions have been considered.

混合分布的一种估计程序AI 解读

Notation The symbols for estimators in this paper have been printed in light italic type. This is an exception from our usual typographic convention of showing matrices and vector quantities in bold black type, since in this case the large number of such symbols would seriously interfere with readability. Summary A general method is proposed for estimating the mixing measures of combinations of known distributions. The method is applicable to continuous and discrete…

关于匹配样本卡方检验的注记AI 解读

Summary This note represents an extension of the author's results (Bennett, 1967) on the problem of tests for matched samples. These were shown to be equivalent to tests of linear hypotheses H0 concerning multinomial probabilities. Solutions for the goodness-of-fit and modified minimum chi-square tests and an explicit relation between the two tests are presented. The power function is discussed under certain alternatives to H0.

连续先验下的混合二项分布与概率参数的后验分布AI 解读

Summary Asymptotic expansions are derived for the mixed binomial distribution and the posterior distribution of p for a continuous prior distribution. Expansions are also found for the first four moments of the posterior distribution. Applications to estimation and sampling inspection are discussed.