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两种终端决策与多阶段抽样的贝叶斯决策规则渐近性质：第二部分AI 解读

Summary The paper is a continuation of a paper by the same authors. The model is based on a differentiable prior distribution, a linear loss function, an asymptotically normal sampling distribution and sampling costs proportional to the sample size. Asymptotic expressions are derived for sample sizes, acceptance and rejection criteria and the minimum regret for some k-stage sampling and decision procedures. In the present paper three cases not considered in the previous…

与t检验对应的渐近有效序贯检验AI 解读

Summary Let X1, X2, …, be independent, normally distributed chance variables, each with mean μ and variance σ2, both unknown to the statistician. Let it be required to test sequentially the hypothesis that (make a decision between) μ = μ1 against the alternative μ = μ2, μ1 < μ2. When the sample size is fixed the Student t-test is usually used for this purpose. In the present paper we give a sequential procedure for performing this test which is consistent and asymptotically…

非正态备择下若干两样本位置检验的比较AI 解读

Summary Small to moderate sample size performance of the two-sample χ2, Kolmogorov–Smirnov, Wilcoxon and F-tests of location is investigated in a class of non-normal distributions through Monte Carlo sampling. The class of distributions is that of mixtures of two normal distributions with different means and/or variances. The cases of mixtures considered represent part of the regions for types I, II, IV, VI and VII of the Pearson system of continuous distributions. The…

泊松过程抽样方法的比较AI 解读

Summary Comparison of fixed sampling schemes from a Poisson process is discussed by means of minimum average risk. The best scheme depends upon the loss function, the prior distribution and the cost of sampling which plays a fundamental role in this problem. Also optimum schemes are considered.

最小风险估计量及其应用AI 解读

Summary Methods for obtaining minimum risk estimators with various loss functions and restrictions on the class of estimators are presented. The results are applied to estimators using order statistics and to estimation by graphical procedures. Minimum risk estimators of the Weibull reciprocal-shape parameter that use two order statistics are given.

非线性函数关系的广义最小二乘与最大似然估计AI 解读

Summary A non-linear functional relationship between two mathematical variables is postulated. Departures of observed random variates from the mathematical variable values are assumed to have zero mean and general but known covariance matrix. Assuming normality we obtain by maximum likelihood an expression for the asymptotic covariance matrix of the structural parameter estimates. The expression involves a certain matrix Ψ. A generalized least squares method is proposed…

非参数函数拟合AI 解读

Summary In this note we consider the problem of fitting a general functional relationship between two variables. We require only that the function to be fitted is, in some sense, “smooth”, and do not assume that it has a known mathematical form involving only a finite number of unknown parameters.

对数线性模型分析AI 解读

Summary Log-linear models are extensively used to analyse categorical and “stimulus-response” data. This paper gives an iterative procedure for obtaining maximum likelihood estimates of cell frequencies and of the parameters of a log-linear model in a multinomial experiment.

双样本问题中渐近有效的线性有序秩检验AI 解读

Summary In this paper the nonparametric two-sample problem is considered and tests are proposed for the hypothesis of identity of the two distribution functions. These tests are based on statistics which are linear combinations of ranks of the order statistics of one of the samples, in the two-sample rank order. It is seen that many existing statistics, proposed mainly on heuristic grounds, are members of this class. The asymptotic distribution of such statistics is…

时间序列中的异常值AI 解读

Summary Two models are considered for outliers and their effects in time series. Likelihood ratio and approximate likelihood ratio criteria are derived for these models and the power functions are compared with that of the approach generally applied in the past.

Cramér–von Mises 统计量的分量：第一部分AI 解读

Summary Let Fn(x) be the sample distribution function derived from a sample of independent uniform (0, 1) variables. The paper is mainly concerned with the orthogonal representation of the Cramér-von Mises statistic Wn2 in the form ∑j=1∞(jπ)−2znj2 where the znj are the principal components of n{Fn(x)−x}. It is shown that the znj are identically distributed for each n and their significance points are tabulated. Their use for testing goodness of fit is discussed and their…

不等概率抽样中估计量稳健性与单位标签信息性的研究模型AI 解读

Summary This paper presents a model for investigating how information contained in the labels of a finite population may be utilized in order to reduce variance when sampling from a finite population with varying probabilities. The model assumes a population of N values of a characteristic X given as Xi = Yi + Zi (i = 1, …, N), where the mean of X is to be estimated. Here Yi is a systematic component in the sense that its relation to the label i is a priori known, or…

线性函数关系问题中的似然曲面AI 解读

Summary In a recent paper, Solari has shown that no maximum likelihood solution exists in the linear functional relationship problem. When account is taken of the rounding-off errors in the observations, however, the appropriate likelihood function is bounded and a solution can be found which is approximately maximum likelihood, in the sense that the value of the likelihood at that solution is close to the global supremum. The novel form of this solution is shown and the…

无干扰参数情形下似然比置信集的无偏性AI 解读

Summary Confidence sets based upon the likelihood function are constructed in the case without nuisance parameters. It is shown under certain assumptions on the density function that the confidence sets are unbiased. Various examples are given.

线性开环系统时变性的检验AI 解读

Summary We consider the problem of testing a given open-loop system for time-dependence. The test is based on just a single realization of the input and a single realization of the output. It makes use of the concept of the “evolutionary cross-spectra” of a non-stationary vector process and rests essentially on testing the “uniformity” of a set of vectors, whose components consist of the “evolutionary gain-spectra” and “evolutionary phase-spectra”. Using a logarithmic…

关于 Lehmann 方差齐性检验AI 解读

Summary For testing the equality of variances in k ≥ 2 normal populations Lehmann (1959) proposed a test procedure based on the logarithms of the sample variances. This paper investigates certain properties of that procedure, such as how to determine its critical region for small sample sizes, and whether or not the procedure is unbiased and robust. An asymptotic comparison is also made between Lehmann's test and the more well-known test due to Bartlett (1937).

凸损失在回归设计问题中的应用AI 解读

Summary A general linear regression function is to be observed at n points in order to estimate a known linear combination of the unknown parameters. The n points and the estimator are to be optimum in some sense and in this paper the main criterion for optimality involves uniformly minimizing certain convex loss functions. Three main sets of results are obtained, followed by some further results for normally distributed errors.

回归模型与生命表AI 解读

Summary The analysis of censored failure times is considered. It is assumed that on each individual are available values of one or more explanatory variables. The hazard function (age-specific failure rate) is taken to be a function of the explanatory variables and unknown regression coefficients multiplied by an arbitrary and unknown function of time. A conditional likelihood is obtained, leading to inferences about the unknown regression coefficients. Some generalizations…

弱平稳点过程与随机测度AI 解读

Summary A weakly stationary point process on the real line is a point process with counting measure N(A) defined on Borel subsets A of the real line such that the first two moments of N(A) are finite for bounded Borel sets and invariant under translation. The expected number of points falling in an interval of length u equals μu and serves to define the intensity parameter μ of the process. The variance of the number of points falling in an interval of length u defines the…

有限等待空间M/G/1队列离开过程的协方差结构AI 解读

Summary This paper contains a study of the departure process from M/G/1 queues with a waiting space of size N>0. The property of the departure process which receives the most attention is the covariance of pairs of departure intervals, although a more thorough investigation of the probabilistic structure is undertaken for the case N = 1. A main result of the paper is that in the M/G/1 queue with N = 1, departure intervals separated by one or more intervals are independent.…

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调查抽样回归推断的贝叶斯、信赖与频率学派视角AI 解读

Summary In this paper an attempt is made to show how the regression analysis generally used for hypothetical populations can also be validated for the actual populations commonly dealt with in statistical surveys. This validation is based on a frequency distribution generated by randomization. In this context some comments are made on the relationships between Bayes, fiducial and frequency theories of statistical inference.

可用于累积和控制图的形式表达式AI 解读

Summary The paper describes a number of formal expressions which can be used to determine properties of cumulative sum schemes. Formulae given only depend upon very general assumptions with regard to the distribution of the cumulated statistic. Numerical as well as algebraic procedures are described which permit calculation of the average sample run length to a specified degree of accuracy for almost any statistic likely to arise in practice. Methods for generating the…

若干相互激励点过程的点谱AI 解读

Summary The point spectral matrix is obtained for a class of mutually exciting point processes. The solution makes use of methods similar to those used in solving Wiener–Hopf integral equations.