Topic
Bernoulli sampling
About: Bernoulli sampling is a research topic. Over the lifetime, 354 publications have been published within this topic receiving 10927 citations.
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TL;DR: In this paper, the authors proposed a case-control study in which selection of subjects for full variable ascertainment is based jointly on disease status and on easily obtained "screening" variables that may be related to the disease.
Abstract: A design is proposed for case-control studies in which selection of subjects for full variable ascertainment is based jointly on disease status and on easily obtained "screening" variables that may be related to the disease. Recruitment of subjects follows an independent Bernoulli sampling scheme, with recruitment probabilities set by the investigator in advance. In particular, the sampling can be set up to achieve, on average, frequency matching, provided prior estimates of the disease rates or odds ratios associated with screening variables such as age and sex are available. Alternatively--for example, when studying a rare exposure--one can enrich the sample with certain categories of subject. Following such a design, there are two valid approaches to logistic regression analysis, both of which allow for efficient estimation of effects associated with the screening variables that were allowed to bias the recruitment. The statistical properties of the estimators are compared, both for large samples, based on asymptotics, and for small samples, based on simulations.
96 citations
TL;DR: In this article, the authors proposed novel resampling methods that may be directly applied to variance estimation, which consist of selecting subsamples under a completely different sampling scheme from that which generated the original sample, which is composed of several sampling designs.
Abstract: In complex designs, classical bootstrap methods result in a biased variance estimator when the sampling design is not taken into account. Resampled units are usually rescaled or weighted in order to achieve unbiasedness in the linear case. In the present article, we propose novel resampling methods that may be directly applied to variance estimation. These methods consist of selecting subsamples under a completely different sampling scheme from that which generated the original sample, which is composed of several sampling designs. In particular, a portion of the subsampled units is selected without replacement, while another is selected with replacement, thereby adjusting for the finite population setting. We show that these bootstrap estimators directly and precisely reproduce unbiased estimators of the variance in the linear case in a time-efficient manner, and eliminate the need for classical adjustment methods such as rescaling, correction factors, or artificial populations. Moreover, we show via sim...
92 citations
TL;DR: In this article, the problem of sampling according to a distribution with log-concave density over a convex body was considered, and the sampling is done using a biased random walk, and polynomial upper bounds on the time to get a sample point with distribution close to the distribution were proved.
Abstract: We consider the problem of sampling according to a distribution with log-concave density $F$ over a convex body $K \subseteq \mathbb{R}^n$. The sampling is done using a biased random walk, and we prove polynomial upper bounds on the time to get a sample point with distribution close to $F$.
91 citations
Journal Article•
TL;DR: In this article, the authors proposed a case-control study in which selection of subjects for full variable ascertainment is based jointly on disease status and on easily obtained "screening" variables that may be related to the disease.
Abstract: A design is proposed for case-control studies in which selection of subjects for full variable ascertainment is based jointly on disease status and on easily obtained "screening" variables that may be related to the disease. Recruitment of subjects follows an independent Bernoulli sampling scheme, with recruitment probabilities set by the investigator in advance. In particular, the sampling can be set up to achieve, on average, frequency matching, provided prior estimates of the disease rates or odds ratios associated with screening variables such as age and sex are available. Alternatively--for example, when studying a rare exposure--one can enrich the sample with certain categories of subject. Following such a design, there are two valid approaches to logistic regression analysis, both of which allow for efficient estimation of effects associated with the screening variables that were allowed to bias the recruitment. The statistical properties of the estimators are compared, both for large samples, based on asymptotics, and for small samples, based on simulations.
91 citations
TL;DR: In this article, a method of sequential sampling for grading population level in relation to a critical density is proposed, which is based on the\(\mathop m\limits^* - m\) relationship and can be used without restrictions on the distribution patterns.
Abstract: A method of sequential sampling for grading population level in relation to a critical density is proposed. The method is based on the\(\mathop m\limits^* - m\) relationship and can be used without restrictions on the distribution patterns. The formulae for simple random sampling as well as for two-stage sampling are given.
90 citations