Design of a rotation scheme for a stratified multi-stage sample

A rotation scheme for a stratified multi-stage sample, discussed in this paper, was designed to statisfy the following conditions: (i) there is a constraint on the number of units that can be replaced in each round, and (ii) it is relatively inexpensive to increase the sample size gradually. An example of these conditions was observed in the development of a plan for measuring the accuracy of the billing process of a telephone company. Estimators of the population proportion of elements that possess a specified characteristic are also derived. Each estimator is a weighted average of the corresponding estimates based on the retained units from the original sample and on the new units, where the weight of the estimate based on the new units increases over time. While this rotation scheme is discussed in connection with the billing accuracy of a telephone company, the methodology can be applied to other similar problems.     

Robust designs for ratio and regression estimation

The purpose of this paper is to introduce a class of robust designs to be used with ratio estimators and extend them to regression estimators. Robustness is to be achieved against departures from a model for which the estimator is ‘optimal’. Practical implementation of the design is indicated both for large and small samples.     

Cochran's rule for simple random sampling

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.     

A Note on Confidence Intervals for Proportions in Finite Populations

An exact confidence interval for the number or proportion of successes in a finite population is developed using the standard technique of inverting a family of tests. The resulting procedure is compared with two methods available in the sampling literature and is shown to be equivalent to one of the methods and superior to the other method.     

Semiparametric likelihood-based inference for biased and truncated data when the total sample size is known

Biased and truncated data arise in many practical areas. Many efficient statistical methods have been studied in the literature. This paper discusses likelihood-based inferences for the two types of data in the presence of auxiliary information of known total sample size. It is shown that this information improves inference about the underlying distribution and its parameters in which we are interested. A semiparametric likelihood ratio confidence interval technique is employed. Also some simulation results are reported.     

On a pragmatic modification of survey sampling in three stages

Presented are formulae for an unbiased estimator of a finite population total and an unbiased variance estimator for it when samples are taken by usual procedures in the first two stages with varying probabilities but the third stage units are sampled for economy and convenience in a non-standard way from the pool of all sampled second stage units rather than independently from each of the latter separately containing the former.     

On the Evaluation of the Kolmogorov Statistic

At least two computer program packages, SPSS and STRATA, use simulated Bernoulli trials to draw (without replacement) a random sample of records from a finite population of records. Therefore, the size of the sample is a random variable. Two estimators of a population total under this sampling procedure are compared with the usual estimator under simple random sampling. Conditions under which the Bernoulli sampling estimators have almost the same mean squared error as the simple random-sample estimator are illustrated.