Bernoulli sampling

About: Bernoulli sampling is a research topic. Over the lifetime, 354 publications have been published within this topic receiving 10927 citations.

Statistical applications of the poisson-binomial and conditional bernoulli distributions

Abstract: The distribution of Z1 +···+ZN is called Poisson-Binomial if the Zi are independent Bernoulli random variables with not-all-equal probabilities of success. It is noted that such a distribution and its computation play an important role in a number of seemingly unrelated research areas such as survey sampling, case-control studies, and survival analysis. In this article, we provide a general theory about the Poisson-Binomial distribution concerning its computation and applications, and as by-products, we propose new weighted sampling schemes for finite population, a new method for hypothesis testing in logistic regression, and a new algorithm for finding the maximum conditional likelihood estimate (MCLE) in case-control studies. Two of our weighted sampling schemes are direct generalizations of the "sequential" and "reservoir" methods of Fan, Muller and Rezucha (1962) for simple random sampling, which are of interest to computer scientists. Our new algorithm for finding the MCLE in case-control studies is an iterative weighted least squares method, which naturally bridges prospective and retrospective GLMs.

Robust Estimation in Finite Populations I

Abstract: This is an application of a least-squares prediction approach to finite population sampling theory. One way in which this approach differs from the conventional one is its focus on characteristics of particular samples rather than on plans for choosing samples. Here we study samples in which many superpopulation models lead to the same optimal (BLU) estimator. Random sampling is considered in the light of these results.

The Sampling Distribution of an Estimate Arising in Life Testing

Abstract: This paper deals with the problem of making inferences about the mean of an exponential distribution when the sample is “time-censored”. The exact sampling distribution of the maximum likelihood estimate is obtained and used to show that the asymptotic sampling theory is inadequate unless the sample size is very large. An approximation to the distribution is proposed for use in small samples and compared with a method suggested by Bartlett (1953a). An alternative estimate is suggested which is both simple and highly efficient in certain circumstances. The methods are illustrated by examples.

Design and inference in finite population sampling

Abstract: A Unified Setup for Probability Sampling. Inference in Finite Population Sampling. The Horvitz--Thompson Estimator. Simple Random and Allied Sampling Designs. Uses of Auxiliary Size Measures in Survey Sampling: Strategies Based on Probability Proportional to Size Schemes of Sampling. Uses of Auxiliary Size Measures in Survey Sampling: Ratio and Regression Methods of Estimation. Cluster Sampling Designs. Systematic Sampling Designs. Stratified Sampling Designs. Superpopulation Approach to Inference in Finite Population Sampling. Randomized Response: A Data--Gathering Tool for Sensitive Characteristics. Special Topics: Small Area Estimation, Nonresponse Problems, and Resampling Techniques. Author Index. Subject Index.