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Counting by weighing: construction of two-sided confidence intervals

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Counting by weighing is widely used in industry and often more efficient than counting manually which is time consuming and prone to human errors especially when the number of items is large. Lower confidence bounds on the numbers of items in infinitely many future bags based on the weights of the bags have been proposed recently in Liu et al. [Counting by weighing: Know your numbers with confidence, J. Roy. Statist. Soc. Ser. C 65(4) (2016), pp. 641–648]. These confidence bounds are constructed using the data from one calibration experiment and for different parameters (or numbers), but have the frequency interpretation similar to a usual confidence set for one parameter only. In this paper, the more challenging problem of constructing two-sided confidence intervals is studied. A simulation-based method for computing the critical constant is proposed. This method is proven to give the required critical constant when the number of simulations goes to infinity, and shown to be easily implemented on an ordinary computer to compute the critical constant accurately and quickly. The methodology is illustrated with a real data example.
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Keywords: Confidence bounds; confidence level; confidence set; counting by weighing; statistical inference; statistical simulation

Document Type: Research Article

Affiliations: 1: Department of Mathematics and Statistics, Acadia University, Wolfville, Nova Scotia, Canada 2: S3RI and School of Mathematics, University of Southampton, Southampton, UK 3: Novartis Pharma AG, Basel, Switzerland 4: Department of Statistics and Operations Technology, University of Denver, Denver, CO, USA

Publication date: January 25, 2019

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