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不等概率抽样中方差计算简便的高效估计量AI 解读

For unequal probability sampling designs, design-based variance estimation is cumbersome because it requires second-order inclusion probabilities. For most fixed sample size probability proportional-to-size (φPS) schemes, these probabilities are difficult to compute, and the variance estimation depends on them for a tedious double-sum calculation. We show how to replace the traditional φPS scenario with simpler design/estimator alternatives that preserve the high efficiency…

调查抽样中的广义迭代比例校准程序AI 解读

We propose the name generalized raking for the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables…

调查抽样中的校准估计量AI 解读

This article investigates estimation of finite population totals in the presence of univariate or multivariate auxiliary information. Estimation is equivalent to attaching weights to the survey data. We focus attention on the several weighting systems that can be associated with a given amount of auxiliary information and derive a weighting system with the aid of a distance measure and a set of calibration equations. We briefly mention an application to the case in which the…

小域估计：条件分析AI 解读

In estimating means, totals, and other parameters for small domains of a finite population, the survey statistician is usually faced with a domain sample size that is random rather than controlled at the selection stage. Often a sensible approach is to make design-based inference conditionally on the realized sample size in the domain (nd ). In this article, we suggest and analyze some small domain estimators and their design-based conditional confidence intervals. The…

估计有限总体总量的一般回归估计量方差的加权残差法AI 解读

The paper deals with design based estimation of the variance of the general regression estimator of the finite population total. The usual Taylor linearization variance estimator is an expression in the design weighted regression residuals; in many applications the resulting expression is counterintuitive from a model based standpoint. The improved variance estimator in this paper attaches another simple weight, called ‘g-weight’, to each individual residual. This new…

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…

概率与统计史研究（二十七）AI 解读

This paper follows the development of an aspect of the Theory of Errors known as the Hypothesis of Elementary Errors. This development produced a scientific tradition in statistical inference theory concerned with the causes and effects of nonnormality of statistical data, a tradition sometimes called the Scandinavian school. Its founder was the Swedish astronomer C. V. L. Charlier. Being concerned mainly with the period of Charlier and his followers, this paper first…

通过贝叶斯定理推导一类概率分布AI 解读

Summary Being in some respects expository in character, this paper uses Bayes's theorem to derive a k-variate discrete probability distribution which is fundamental inasmuch as it proliferates, under various sets of asymptotic conditions, to yield as its limiting forms an array of other k-variate distributions including the multinomial, independent Poisson, independent negative binomial, independent gamma, Dirichlet and multivariate normal. A systematic arrangement of these…

若干非参数分布的统一推导AI 解读

This paper presents a unified derivation of a number of parameter-free distributions, some of which have appeared earlier in the literature. The starting point is the information provided by a random sample drawn from a certain population and the frequencies observed in a number of mutually exclusive classes. Several types of populations and several ways of defining the classes are considered. The distributions derived concern the unknown class frequencies and the unknown…