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多项比例的快速同时置信区间AI 解读

Opinion polls often give an indication of sampling error based on the standard conservative confidence intervals for a single binomial proportion. We give a lower bound for the simultaneous coverage probability when such intervals are applied to all of the proportions in a poll. This bound is equal to 1 – 2α. for small values of α. The same result is shown to apply to the standard confidence intervals for changes in proportions between surveys.

比率与回归估计量的渐近分布AI 解读

We give a formal derivation of the asymptotic normality of ratio and regression estimators of a finite population total for simple random sampling and for sampling with probability proportional to aggregate size. The results are all well known and widely used, of course, but a rigorous development, spelling out relatively simple sufficient conditions under which the standard results are valid, does not seem to be available at present.

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调查设计、对称性与后验分布AI 解读

Summary It is now well known that the sample design is irrelevant in a Bayesian analysis of survey data provided the units are labelled and the sampling is non-informative. However, information about the labels is often not available for the analysis, and in this situation the design will contain information about the labelling and hence affect the inferences. There is one important exception: if the prior distribution is exchangeable and we are interested only in symmetric…

多阶段调查中的估计AI 解读

A superpopulation model is proposed for two-stage sampling from a finite population and we consider the problem of estimating a linear function of the finite population elements. We find the estimate with smallest mean squared error among linear estimates with bounded mean squared error without any assumption about the form of the super-population distribution. If the superpopulation is assumed to be normal this estimate is the mean of the posterior distribution. The…