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Beta–Stacy 分布尺度参数估计量的比较AI 解读

The Beta-Stacy distribution was defined in [1]. In this distribution X1 has a generalized gamma distribution, while the conditional distribution of X2 given X1 is beta with range 0 to X1. Estimation of a scale parameter of the distribution of X1, using only observations on X2, is discussed. Corrections to formulas in [1] are given.

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Theil 混合回归估计量的若干有限样本结果AI 解读

Finite sample properties of Theil's mixed regression estimator and test statistic for checking the compatibility of prior and sample information, are studied via Monte Carlo sampling experiments.

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调查数据处理一次抽样检验方案中的核验误差AI 解读

This article deals with measurement error in single sampling inspection plans of the attributes type. Formulas are provided to assess the effect of inefficient inspection and correction on the power of the sampling plan to distinguish between acceptable and unacceptable quality levels, on average outgoing quality, and on costs. Emphasis is placed on the error of classifying defectives as nondefectives (Type II) made by both inspectors (called “verifiers”) of sample items and…

用一般线性统计模型对经济数据进行季节调整AI 解读

This article presents a technique of seasonal adjustment of economic time series within the framework of the general linear statistical model. The technique is designed to be flexible enough to be applicable to varying types of economic time series. The first goal of the technique is the development of a specification that allows adequate flexibility in the estimation of the trend-cycle component of a time series. The second goal is the development of a method of handling…

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接收抽样方案 OC 曲线下公平质量水平与误差面积的理论AI 解读

The concepts of “equitable quality level” (EQL) and “error-areas” are defined in terms of the operating characteristic and the prior distribution of incoming lot quality. Asymptotic expansions are obtained for them in terms of derivatives of the prior distribution and moments of an auxiliary random variable, the latter depending only on the elements of the sampling plan. It is indicated how these results can be of use in constructing plans having certain optimum properties.

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快速计算基于秩的有效估计量及其渐近效率AI 解读

A class of simple methods of computing asymptotically efficient estimates which are asymptotically equivalent to centers of the confidence intervals from rank tests for a location parameter is described. Values of the asymptotic efficiencies are given for populations other than that used for construction of a particular estimate.

正态分布标准差与方差比的最短区间表AI 解读

Tables are presented for Bayes shortest posterior intervals on the standard deviation and variance ratio of normal distributions. A general procedure for obtaining such intervals is reviewed, and a discussion of frequentist shortest intervals is given along with frequentist interpretations of the intervals from these tables.

线性支出系统的最大似然估计AI 解读

The linear expenditure system provides a convenient model for representing consumer response to prices and income. The parameters of the model enter nonlinearly and standard estimation procedures lack desirable properties. This note discusses the problems with existing techniques and derives the maximum-likelihood estimators. The linear expenditure system (LES) was proposed and applied by Stone [7, 8], and it has found further application in [9], [2], and [4]. Aspects of the…

包含概率与规模成比例的抽样设计及 Horvitz–Thompson 估计量AI 解读

Using the criterion of minimum expected variance and the Horvitz-Thompson estimator, we study various πPS (πi, the probability of inclusion of the ith unit, Proportional to Size) strategies and make a comparison between these strategies under a general super population model. This discussion further motivates the search for a class of designs which are best suited for the use of the Horvitz-Thompson estimator. A new class of such designs is obtained.

似然比的保守置信区间AI 解读

A method is described for assigning an observation to one of two normal populations with differing, unknown means and differing, unknown variances. The classification procedure rests on the likelihood ratio, which, for a given observation, is a function of four unknown parameters. Sample information is used to obtain a confidence region for these parameters. From this confidence region, a conservative confidence interval for the likelihood ratio is derived. Interpreting the…

加速寿命试验中的一个估计问题AI 解读

Parameters of the Power Rule Model are estimated using data from censored sample life tests conducted at accelerated environments. By amending the functional form of the model, it is possible to obtain estimators that are asymptotically independent. The asymptotic normality of these estimators is ascertained by examining the shapes of their relative likelihood functions. Approximate confidence intervals, and an exact plausibility interval for the mean life (exponential case)…

限制贝叶斯与经验贝叶斯估计量的风险：第一部分，贝叶斯情形AI 解读

The first part of this article considers the Bayesian problem of estimating the mean, θ, of a normal distribution when the mean itself has a normal prior. The usual Bayes estimator for this situation has high risk if θ is far from the mean of the prior distribution. We suggest rules which do not have this bad property and still perform well against the normal prior. These rules are compromises between the Bayes rule and the MLE. Similar rules are suggested for the empirical…

Fisher 独立检验合并方法的渐近最优性AI 解读

Four methods of combining independent tests of hypothesis are compared via exact Bahadur relative efficiency. The methods considered are Fisher's method, the mean of the normal transforms of the significance levels, the maximum significance level, and the minimum significance level. None of these is uniformly more powerful than the others, but, according to Bahadur efficiency, Fisher's method is the most efficient of the four. In some cases, Fisher's method is most efficient…

卡方统计量常见样本量使用限制的考察AI 解读

This empirical study of the chi-square approximations as commonly encountered in behavioral research involved: (1) both tests of goodness-of-fit and of independence, (2) uniform distributions and two levels of departure from uniform, (3) sample sizes ranging from 10 to 100. Excellent approximations were obtained with average expected frequencies of one or two in tests of goodness-of-fit to uniform; slightly higher expected frequencies were required with the non-uniform…