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对 Choi 与 Bulgren《分布混合的估计程序》的评论AI 解读

Summary Choi and Bulgren's (1968) estimator for the mixing measure of a mixture of known distributions is biased in small samples; a variant of their estimator has a much smaller bias, and a smaller mean squared error, for mixtures of normal distributions differing in mean. The maximum-likelihood estimator is shown to be more computable than Choi and Bulgren suggest. Estimation is much more difficult when the component distributions are unknown; for example, a mixture of two…

簇点过程的存在性与混合性质AI 解读

Summary Cluster point processes are defined and studied using the probability generating functional. Necessary and sufficient conditions for the existence of a cluster process are proved and applied to particular cases. A result on mixing in cluster processes is established.

人口模型中转移强度的点估计AI 解读

Summary Occurrence/exposure rates are developed as estimators for the forces of transition of a homogeneous, time-continuous Markov process with at most countable state space in the case where the number of such forces is finite. Conditions for consistency and asymptotic normality of the estimators are stated.

从似然函数构造区间估计AI 解读

Summary During the last few years, several authors have devoted attention to both old and new methods of making inferences from likelihood functions. In this paper we study the properties of interval estimates which are obtained by drawing a horizontal line across the graph of the likelihood function. An exact evaluation is reported for one case of positive and one of negative binomial sampling, with parameter θ. The attained confidence coefficient α(θ) is graphed over 0 ⩽ θ…

回归分析中的同时置信带AI 解读

Summary Simultaneous confidence intervals for linear combinations of parameters in a regression analysis are discussed, and a desirable property is described. Confidence intervals having this property are characterized and the Working–Hotelling band is discussed with reference to it. It is shown how this band may be sharpened to give exact confidence levels in linear and quadratic regression. Tables are given from which the confidence bands may be constructed.

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平稳多元时间序列的若干独立性检验AI 解读

Summary Let X(t)=(X1(t)X2(t)⋮XP(t)),t=⋯−1,0,1…, be a p-dimensional zero-mean stationary Gaussian time series possessing a spectral density matrix F(ω) = {fij(ω)}, i, j = 1, 2, …, p, satisfying some mild regularity conditions. Let F^(ωl), l=1, 2, … ,M, F^(ωl)={f^ij(ωl)} be suitably defined sample spectral density matrices for M values of ω, based on a record of length T ≫ M. We consider the following (null) hypotheses: H1: Xi(t), Xi(s) independent if i ≠ j, all s, t, H2:…

自回归移动平均误差回归模型中残差自相关的分布AI 解读

Summary In examining the adequacy of a statistical model an analysis of the residuals is often carried out; and for models involving a time series structure the serial correlations of the residuals are natural statistics to consider. In this paper it is shown that asymptotically the first s sample autocorrelations of the residuals, calculated from a least-squares fit of a regression model in which the errors follow a stationary autoregressive–moving average time series,…

关于秩方差分析的一个统计量AI 解读

Summary Gabriel and Sen (1968) have presented a family of statistics for univariate and multivariate one-way rank analysis of variance. The present note considers the univariate Gabriel–Sen statistic of the Mann–Whitney family. An elementary derivation of its asymptotic null distribution is pointed out. It is shown that simultaneous testing procedures (s.t.p.) based on the above statistic are asymptotically coherent.

区组设计与缺失数据AI 解读

Summary The fitting of missing plot values is considered for the general case of block designs. A method is given for their direct calculation using the design matrices. An iterative method is recommended and is compared with others already in use. Two expressions are given for the covariance matrix of adjusted treatment means when data are incomplete.

复相关系数抽样分布的若干结果AI 解读

Summary Recurrence formulae for the density function and the probability integral of the multiple correlation coefficient from a normal sample are obtained. When the number of independent variates is odd these formulae are related to the distribution of the simple correlation. Asymptotic expansions in terms of the non-central beta and of the non-central χ2 distributions are derived. Methods of approximation by the central and the non-central F distributions, as well as by…

虚拟变量向量空间中判别函数的拟合优度AI 解读

Summary The problem of discrimination among several groups can be looked upon as the problem of “association” between the vector of variables under consideration and a vector of “dummy” variables representing the contrasts among the groups. In certain situations, observations on one or more of these dummy variables are explicitly available and tests have been derived by Bartlett and Williams, for the adequacy of a set of assigned discriminant functions from among these dummy…

非正态分布的后验精度AI 解读

Summary The result “average posterior precision equals or exceeds prior precision plus average observation precision” is proved for any distributions of a single variable. The “average” used is in effect a harmonic mean.

依赖观测下最大似然估计的渐近性质AI 解读

Summary The problem of weak consistency and asymptotic efficiency of the maximum-likelihood estimate in the case of dependent random variables (observations) is considered. A set of readily applicable conditions that ensure these properties of the maximum-likelihood estimate is presented. The conditions are expressed in terms of the probability density distribution of individual observations, conditioned upon all past observations. The connection between these conditions and…

线性函数关系似然曲面的鞍点AI 解读

Summary In a recent paper Solari has shown that there is no maximum-likelihood solution to the problem of estimating a linear functional relationship when both variates are subject to errors that have an unspecified bivariate normal distribution. The estimators purporting to be maximum-likelihood estimators were shown by Solari to determine a saddle point. This discovery clears up some anomalies that have been noted in the past.

将出生过程变换为泊松过程AI 解读

Summary The pure birth process with linear birth rates is considered. The sum of sojourn times is shown to have a functional relationship with an asymptotic estimate of the population size that is known from the theory of branching processes. A theorem concerning this estimate, due to Kendall (1966), is proved by means of this relationship, in a way which brings out the connection between Kendall's theorem and an important property of non-time-homogeneous Poisson processes.…

列联表关联度量：交叉比与度量方法的三项扩展AI 解读

Summary The methods of cross-ratios, equivalence classes and metrics that were introduced in a previous paper (Altham 1970) are extended to three further problems. First the interdependence of the rows, columns and layers of a three-way contingency table is discussed. There are essentially four different types of association to be considered: the complete dependence of rows, columns and layers, the dependence of rows and columns conditional on a given layer, the dependence…

复相关系数分布的进一步研究AI 解读

Summary A general class of series expansions for the non-null distribution of the multiple correlation coefficient is presented which contains, as special cases, the three expansions obtained by one of the authors (Gurland, 1968). The rate of convergence is investigated, and the closeness of an approximation to the true distribution is indicated.

随机缺失观测下的谱分析AI 解读

Summary Spectral analysis of data with randomly missing observations is considered. Conditions are found under which consistent estimation of the spectral density function of the observed process is possible. An estimate is proposed and the results of a simulation study of its first two moments are presented.

随机变量线性函数的参数估计AI 解读

Summary Let W be a random variable and X be a linear function of W: X = αW + β. Given a sample of independent observations distributed as X, we wish to find maximum-likelihood estimators for the parameters α and β of the linear function. If the support of W is the whole real axis, the maximum-likelihood estimators can be found by the usual methods; in other cases restricted maximization techniques must be used. Here we restrict attention to cases in which the support is the…

含时变参数的非平稳时间序列模型拟合AI 解读

Summary We use the method of weighted least squares to estimate the time-dependent parameters of non-stationary time-series models. Approximate expressions for the bias and variance of the estimates, which could be used to assess the merits of various weight functions on the basis of “mean square error” criterion, are obtained. In Section 5, it is shown that the estimates obtained by weighted least-squares method are the same as estimates obtained by weighted…

Durbin 的新多阶段抽样方差估计量AI 解读

Summary A new variance estimator was suggested implicitly by Durbin (1967), for use in a particular multistage sampling procedure. The suggestion can easily be extended to cover the general case in which selection at the first stage is without replacement (the probabilities of inclusion in sample being arbitrary) and in which unbiased estimators are used at all stages of sampling. As compared with the earlier Durbin multistage variance estimator, the new estimator has this…

Summary The problem of obtaining consistent estimates for structural parameters in the presence of infinitely many incidental parameters was discussed first by Neyman and Scott (1948). In this paper a maximum-likelihood method based on the conditional distribution given minimal sufficient statistics for the incidental parameters is suggested. It is proved that conditional maximum-likelihood estimates in the regular case are consistent and asymptotically normally distributed…

多个正态总体最大均值的多阶段区间估计AI 解读

Summary We have k normal populations (k ⩾ 1) with means θ1, θ2, …, θk and a common unknown variance σ2. A fixed-width confidence interval for θ*=max⁡1≤i≤k θi is desired so that the coverage probability is at least γ (preassigned) for every θ = (θ1, θ2, …, θk) and σ2 > 0. A class of multistage procedures is considered for the solution of this problem. It is shown that at least for k ≤ 2, the efficiencies of those procedures are always less than one.