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Counting by weighing: construction of two-sided confidence intervals

Counting by weighing: construction of two-sided confidence intervals
Counting by weighing: construction of two-sided confidence intervals

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.

Confidence bounds, confidence level, confidence set, counting by weighing, statistical inference, statistical simulation
0266-4763
1-10
Peng, J.
6267e5fb-f81f-4f04-a4a1-49741596e330
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9
Peng, J.
6267e5fb-f81f-4f04-a4a1-49741596e330
Liu, W.
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, A.J.
55bd07a5-db1d-4d3d-8c87-b307485420d9

Peng, J., Liu, W., Bretz, F. and Hayter, A.J. (2018) Counting by weighing: construction of two-sided confidence intervals. Journal of Applied Statistics, 1-10. (doi:10.1080/02664763.2018.1475553).

Record type: Article

Abstract

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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Counting by weighing - Accepted Manuscript
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Accepted/In Press date: 27 April 2018
e-pub ahead of print date: 18 May 2018
Keywords: Confidence bounds, confidence level, confidence set, counting by weighing, statistical inference, statistical simulation

Identifiers

Local EPrints ID: 421916
URI: http://eprints.soton.ac.uk/id/eprint/421916
ISSN: 0266-4763
PURE UUID: a2486347-f059-48fd-965a-7d4dab48808b
ORCID for W. Liu: ORCID iD orcid.org/0000-0002-4719-0345

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Date deposited: 09 Jul 2018 16:30
Last modified: 16 Mar 2024 06:44

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Contributors

Author: J. Peng
Author: W. Liu ORCID iD
Author: F. Bretz
Author: A.J. Hayter

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