Topic
Population proportion
About: Population proportion is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4099 citations.
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TL;DR: In this article, the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit, is discussed, and three probit models are used.
Abstract: This article discusses the estimation of a population proportion, using the auxiliary information available, which is incorporated into the estimation procedure by a probit model fit. Three probit ...
2 citations
TL;DR: In this article, a predictive estimator is proposed which incorporates the auxiliary information at the estimation stage by invoking a superpopulation model, and a bootstrap-based hybrid re-sampling method is developed.
Abstract: Suppose that a finite population consists of N distinct units. Associated with the ith unit is a polychotomous response vector, d
i
, and a vector of auxiliary variable x
i
. The values x
i
’s are known for the entire population but d
i
’s are known only for the units selected in the sample. The problem is to estimate the finite population proportion vector P. One of the fundamental questions in finite population sampling is how to make use of the complete auxiliary information effectively at the estimation stage. In this article a predictive estimator is proposed which incorporates the auxiliary information at the estimation stage by invoking a superpopulation model. However, the use of such estimators is often criticized since the working superpopulation model may not be correct. To protect the predictive estimator from the possible model failure, a nonparametric regression model is considered in the superpopulation. The asymptotic properties of the proposed estimator are derived and also a bootstrap-based hybrid re-sampling method for estimating the variance of the proposed estimator is developed. Results of a simulation study are reported on the performances of the predictive estimator and its re-sampling-based variance estimator from the model-based viewpoint. Finally, a data survey related to the opinions of 686 individuals on the cause of addiction is used for an empirical study to investigate the performance of the nonparametric predictive estimator from the design-based viewpoint.
2 citations
07 Dec 2008
TL;DR: This work considers a methodology developed for Bayesian reliability analysis, where historical data is used to define the a priori distribution of proportions p, and the customer desired a posteriori maximum probability is utilized to determine sample size for a replication.
Abstract: Limit standards are probability interval requirements for proportions. Simulation literature has focused on finding the confidence interval of the population proportion, which is inappropriate for limit standards. Further, some frequentist approaches cannot be utilized for highly reliable models, or models which produce no or few non-conforming trials. Bayesian methods provide approaches that can be utilized for all limit standard models. We consider a methodology developed for Bayesian reliability analysis, where historical data is used to define the a priori distribution of proportions p, and the customer desired a posteriori maximum probability is utilized to determine sample size for a replication.
2 citations
31 Dec 2009
TL;DR: The property of the Wald interval is investigated in terms of the coverage probability and the expected width, and an alternative confidence interval based on the Agresti-Coull's approach is recommended.
Abstract: The double sampling scheme is effective in reducing the sampling cost However, the doubly sampled data is contaminated by two types of error, namely false-positive and false-negative errors These would make the statistical analysis more difficult, and it would require more sophisticate analysis tools For instance, the Wald method for the interval estimation of a proportion would not work well In fact, it is well known that the Wald confidence interval behaves very poorly in many sampling schemes In this note, the property of the Wald interval is investigated in terms of the coverage probability and the expected width An alternative confidence interval based on the Agresti-Coull's approach is recommended
2 citations
TL;DR: In this paper, the problem of estimating the population proportion of a categorical variable using the calibration framework is considered, and a new class of estimator based upon the proposed calibration estimators is also defined, and the optimal estimator in the class, in the sense of minimal variance, is derived.
Abstract: This paper considers the problem of estimating the population proportion of a categorical variable using the calibration framework. Different situations are explored according to the level of auxiliary information available and the theoretical properties are investigated. A new class of estimator based upon the proposed calibration estimators is also defined, and the optimal estimator in the class, in the sense of minimal variance, is derived. Finally, an estimator of the population proportion, under new calibration conditions, is defined. Simulation studies are considered to evaluate the performance of the proposed calibration estimators via the empirical relative bias and the empirical relative efficiency, and favourable results are achieved.
2 citations