Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T12:19:05.725Z Has data issue: false hasContentIssue false
  • English
  • Français

Matched pairs in independent Poisson processes

Published online by Cambridge University Press:  14 July 2016

David Oakes
David Oakes*
Affiliation:
London School of Hygiene and Tropical Medicine
*
∗Postal address: TUC Centenary Institute of Occupational Health, London School of Hygiene and Tropical Medicine, Keppel St (Gower St), London WC1E 7HT, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

Given two independent Poisson processes 𝒜 and ℬ with rates respectively α and β (α < β) we match each point of 𝒜 with the closest point of ℬ that has not already been matched. The points of 𝒜 are taken in random order. It is shown that the point process of unmatched points of ℬ is a renewal process with the same interval distribution as the busy period of an M/M/1 queue. The distribution and moments of the distance between a typical point of 𝒜 and the corresponding matched point of ℬ are obtained. Variants of the matching process in which the assigned point of ℬ must lie to the right of the point of 𝒜, and in which the matching distance must be less than a fixed tolerance are studied. The use of matched samples to control for bias in observational studies is discussed.

Keywords

MATCHINGPAIR-MATCHINGCALIPER MATCHINGNEAREST AVAILABLE MATCHINGBUSY PERIOD
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 780 - 793
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Carpenter, R. G. (1977) Matching when covariables are normally distributed. Biometrika 64, 299–307.Google Scholar
Cochran, W. G. and Rubin, D. B. (1973) Controlling bias in observational studies: A review. Sankhya A 35, 417–446.Google Scholar
Coleman, R. (1974) Nearest neighbour distances for equilibrium renewal processes. Adv. Appl. Prob. 6, 220.Google Scholar
Cox, D. R. and Lewis, P. A. W. (1966) The Statistical Analysis of Series of Events. Methuen, London.Google Scholar
Cox, D. R. and Smith, W. (1961) Queues. Chapman and Hall, London.Google Scholar
Daley, D. J. (1964) Single-server queueing systems with uniformly limited queueing time. J. Austral. Math. Soc. 4, 489–504.Google Scholar
Mckinlay, S. (1974) The expected number of matches and its variance for matched pair designs, Appl. Statist. 23, 372–383.Google Scholar
Rubin, D. B. (1973a) Matching to remove bias in observational studies. Biometrics 29, 159–183.Google Scholar
Rubin, D. B. (1973b) The use of matched sampling and regression adjustment to remove bias in observational studies. Biometrics 29, 185–203.Google Scholar
Rubin, D. B. (1976a) Multivariate matching methods that are equal percent bias reducing I: Some examples. Biometrics 32, 109–120.CrossRefGoogle Scholar
Rubin, D. B. (1976b) Multivariate matching methods that are equal percent bias reducing II: Maximums on bias reduction for fixed sample sizes. Biometrics 32, 121–132.Google Scholar