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Cochran's Rule for Simple Random Sampling

简单随机抽样中的 Cochran 规则

Summary Cochran's rule for the minimum sample size to ensure adequate coverage of nominal 95% confidence intervals is derived by using the Edgeworth expansion for the distribution function of the standardized sample mean. The rule is extended for confidence intervals based on the Studentized sample mean. The performance of the rule and Edgeworth approximations for smaller sample sizes are examined by simulation.

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The Effect of Sample Design on Principal Component Analysis

抽样设计对主成分分析的影响

Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic…

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The Effect of Sample Design on Principal Component Analysis

抽样设计对主成分分析的影响

Most sample surveys are multivariate and many lend themselves to multivariate methods of analysis. The most usual mode of such analysis is a standard statistical package, such as BMDP or SPSS, in which the multivariate analyses are based on the underlying assumption that the data are generated as independent observations from a common probability distribution. This assumption ignores the sample selection procedure involved in the survey, which leads to the following basic…

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The effect of sample design on the comparison of associations

抽样设计对关联比较的影响

A family of measures of association designed to compare the inherent association in two r×c contingency tables was proposed by Altham (1970). Under simple random sampling the measures are asymptotically distributed as noncentral chi-squared random variables. In this paper we show that under complex sampling this distribution changes to a mixture and that ignoring the design may lead to misleading results. We derive measures of the misestimation and measures of association…

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Ignorable and Informative Designs in Survey Sampling Inference

调查抽样推断中的可忽略与信息性设计

The role of the sample selection mechanism in a model-based approach to finite population inference is examined. When the data analyst has only partial information on the sample design then a design which is ignorable when known fully may become informative. Conditions under which partially known designs can be ignored are established and examined for some standard designs. The results are illustrated by an example used by Scott (1977).

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Ignorable and informative designs in survey sampling inference

调查抽样推断中可忽略与信息性设计

The role of the sample selection mechanism in a model-based approach to finite population inference is examined. When the data analyst has only partial information on the sample design then a design which is ignorable when known fully may become informative. Conditions under which partially known designs can be ignored are established and examined for some standard designs. The results are illustrated by an example used by Scott (1977).

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Minimax designs for sample surveys

抽样调查中的极小极大设计

Blackwell & Girshick (1954) have shown that simple random sampling is the minimax sampling strategy when the quantity being estimated and the space of possible population values are suitably eymmetric. In this paper, sampling with probabilities proportional to size is shown to be the minimax strategy under fairly strong conditions when the quantity being estimated is not symmetric.

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Minimax Designs for Sample Surveys

抽样调查的极小极大设计

Blackwell & Girshick (1954) have shown that simple random sampling is the minimax sampling strategy when the quantity being estimated and the space of possible population values are suitably eymmetric. In this paper, sampling with probabilities proportional to size is shown to be the minimax strategy under fairly strong conditions when the quantity being estimated is not symmetric.

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Analysis of Repeated Surveys Using Time Series Methods

利用时间序列方法分析重复调查

Standard time series methods are applied to the analysis of repeated surveys under the assumption that the population parameters at each time period follow a stochastic model. Both overlapping and nonoverlapping surveys are considered in general terms, and specific results are obtained for the time series models assumed in the work of Patterson [10].

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Survey Design, Symmetry and Posterior Distributions

调查设计、对称性与后验分布

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…

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Estimation in Multi-Stage Surveys

多阶段调查中的估计

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…

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