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数据编辑中识别错误的概率模型AI 解读

Certain data screening systems incorporate large numbers of logical checks on data entering the system. When violated, these logical checks indicate that various combinations of variates are in error. This article provides a model for assigning a probability measure to identify variates in error when there is a simultaneous violation of a set of logical checks. For certain symmetry conditions, the measure is a reasonable approximation to the posterior probability that given…

双变量均有误差且均值排序已知时的直线拟合AI 解读

Two methods, one based upon grouping, are proposed for fltting a regression line to bivariate data when the means of the observations have known order along the line. The two procedures are compared with respect to their limiting distributions and asymptotic efficiency. Criteria are given for choosing one of these procedures to fit the line.

位置参数的渐近最优分组秩检验AI 解读

The asymptotic efficiency of a simple group rank test is examined in the case of testing that the location parameter of a symmetric distribution is zero against the alternative it is positive. Asymptotic optimality is shown subject to a condition on the density function. Efficiencies in relation to the sample mean and the sign test are found in several cases.

具有随机进入与退出机制的马尔可夫链推断AI 解读

Models suitable for statistical inference in Markov chains are considered featuring various forms of stochastic entry, including Poisson, renewable binomial pool, uncertain pool size, negative binomial, and input-output reservoir. A parallel inactive states model is suggested for exit. Maximum likelihood estimates are obtained and likelihood ratio tests derived. An application is made to the distribution of Ninth Federal Reserve District member banks with respect to the…

指数生存曲线的序贯比较AI 解读

A general approach is outlined to the problem of sequentially comparing exponential “survival” curves in a clinical trials setting. It entails applying sequential tests of hypotheses concerning the drift of a Wiener process to a particular discrete-time process generated from the survival data. Anderson's [1] modified sequential probability ratio test [SPRT) is used for illustration. Monte Carlo studies indicate that the method is valid for samples of moderate size and that…

将分层抽样中的样本分配视为博弈AI 解读

We consider here the problem of allocating sampling effort among strata when there is no useful information on the within-stratum variability. We show that in a natural game theoretic analogue proportional allocation is a unique good strategy.

方差分析第二类模型中的均方合并AI 解读

This article presents a procedure for estimating the true error variance σ2 3 after two preliminary tests of significance in ANOVA Model II and considers its comparison as regards to bias and mean square error with that of an unbiased estimator of σ2 3.

删失回归样本的参数估计AI 解读

Winsorization and trimming using stratified and pooled procedures are proposed for linear regression analysis. The regression model assumes an equal number of observations at each value of an equally spaced independent variable. In the null case, the error variable is normally distributed. Efficiencies of estimates are obtained analytically for the stratified procedure and by Monte Carlo methods for the pooled procedure. Means and variances of estimates are obtained…

最小二乘估计量分布与扰动项分布的 Pearson 系数关系AI 解读

In this note we derive the third and fourth moments of ordinary least squares estimators of coefficients in a general linear regression model without making any assumption regarding the form of distribution of the disturbance term. These results are then used to establish a relationship between Pearsonian coefficients of the distributions of least squares estimators and the disturbance term.

正态变量二次型分布的一类新界AI 解读

Except in special cases, the distribution of a quadratic form Q in the normal random vector y cannot be expressed in closed form. However, bounds on the cumulative distribution of Q have been obtained by many authors. This article derives a new class of such bounds by means of a certain mixture representation for the distribution of Q. It is shown how the results apply to the problem of finding the distribution of ratios of independent quadratic forms in normal variates.

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参数由独立样本估计时的卡方检验AI 解读

If the parameters are estimated independently of the sample, the chi-square test statistic for a goodness of fit test has a limiting distribution that is stochastically larger than that of the test of fit for a completely specified distribution. Thus, if the critical values for the test of fit for a completely specified distribution are incorrectly used, the probability that we will reject the null hypothesis when it is true is greater than the desired level of significance.

分类数据趋势检验中的分组方法AI 解读

In many studies there is believed to be a trend in a categorical variate with a continuous variate. Often in these cases it is desired to test for the trend using k groups formed from the continuous variable. This article is concerned with the grouping problem where the goal is essentially to maximize the asymptotic efficiency of the test. Optimal classes are given for k = 2, 3, 4, 5 and 6 for the uniform, normal and exponential distributions. Also, the number of groups to…

随机模型假设检验中卡方与似然比检验的小样本功效比较AI 解读

When applying the Markov model, it is often assumed the transition matrix is stationary and of order one. This article considers the problem of applying the transformed likelihood ratio statistic and the contingency statistic to testing the assumptions of a particular order and of stationarity when the assumptions are not true. A Monte Carlo study of the small sample power of both these test statistics shows that if the true alpha level is kept equal for the two tests they…

美国石油炼制业的经济—线性规划模型AI 解读

The linking of statistically estimated relationships with an engineering linear programming model offers important potentials for simulation and forecasting models of industries. This article describes such a model of the U.S. petroleum refining industry. Econometric techniques are used to specify product demands, prices, and some technical adjustments. A linear programming specification of the production function, assuming cost minimization, determines crude oil input…

两个正态密度混合模型中矩估计与最大似然估计的比较AI 解读

Assuming common variance, the moment estimators of a mixture of two normal densities are obtained. The asymptotic covariance matrix of the moment estimators and the information matrix are then derived and hence the efficiency of the moment method computed.

利用秩统计量构造置信集AI 解读

Systematic procedures for constructing confidence bounds and point estimates based on rank statistics are given for the two sample location parameter, two sample scale parameter and one sample location parameter problems.

二项序列同质性检验的功效AI 解读

Approximations to the power functions of the classical X2 test and the locally asymptotically optimal test of homogeneity of a binomial series are obtained for the case of known binomial parameter; asymptotic power functions are also derived. The results are compared with values of power obtained by simulation.

Theil 的 BLUS 残差的最优性性质AI 解读

In the linear model y=Xβ+u, the error vector u is not observable. Following Theil [8] we approximate J'u, a vector of selected components of u, by A'y with A chosen so that ϵ(A'y) = 0 and U(A'y) = σ2I. We study Σa = U(A'y—J'u) and give a new proof that fr Σa is minimized at A = B, where B'y is the vector of BLUS residuals. The claim in [9] that Σa — Σb is positive semi-definite is shown not to hold in general; we prove, however, that the BLUS residuals minimize each…

选择最佳正态总体时多因素实验相对多个单因素实验的渐近效率AI 解读

In this article, we consider two single-stage procedures for ranking means of normal populations with a common known variance, for problems involving an r-way (r≧2) classification without interaction. For the problem of selecting the best level of each of the r factors, the asymptotic (p*→7) efficiency of one r-factor experiment relative to r one-factor experiments is determined. Applications to some related problems are noted.

重新考察平稳随机回归参数的估计AI 解读

This article reexamines the problem of estimation in repeated regression experiments wherein the regression parameters vary according to a stationary stochastic process with known covariance structure. Best linear unbiased estimators, more efficient than those recently proposed by Burnett and Guthrie, are derived.

尺度参数的 Λ-minimax 估计AI 解读

This note illustrates the application of the Λ-minimax principle (see, e.g., [6, Sect. 6.6]) to the estimation of a scale parameter. In particular, σ Λ-minimax estimator of the variance of a normal distribution is obtained when Λ is a subset of the class of natural conjugate prior distributions. Two cases considered are (1) the mean is known and (2) a fully specified prior distribution is available for the mean. Case 2 is reduced to Case 1.

多元位置参数的 Λ-minimax 估计AI 解读

The search for a linear Λ-minimax estimate (see, e.g., [19]) of a multivariate location parameter (with quadratic loss) is reduced to a problem of maximizing a continuous function on a compact, convex set—a problem which can be solved numerically with little difficulty. This reduction is accomplished by showing that a minimax theorem applies, thus changing a difficult minimax calculation to a simpler maximin problem. The technique is observed to be applicable to other,…