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Issue ESAIM: PS
Volume 10, 2006
Page(s) 11 - 23
DOI 10.1051/ps:2005019
Published online 16 December 2005

ESAIM: P&S, January 2006, Vol. 10, pp. 11-23
DOI: 10.1051/ps:2005019

Using auxiliary information in statistical function estimation

Sergey Tarima1 and Dmitri Pavlov2

1  Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, Wisconsin, 53226, USA; starima@hpi.mcw.edu
2  Clinical Biostatistics, Pfizer Inc., 50 Pequot Avenue, New London, Connecticut, 06320, USA; dmitri.pavlov@pfizer.com


(Received February 28, 2004. Accepted July 22, 2005 / Published online: 16 December 2005)

Abstract
In many practical situations sample sizes are not sufficiently large and estimators based on such samples may not be satisfactory in terms of their variances. At the same time it is not unusual that some auxiliary information about the parameters of interest is available. This paper considers a method of using auxiliary information for improving properties of the estimators based on a current sample only. In particular, it is assumed that the information is available as a number of estimates based on samples obtained from some other mutually independent data sources. This method uses the fact that there is a correlation effect between estimators based on the current sample and auxiliary information from other sources. If variance covariance matrices of vectors of estimators used in the estimating procedure are known, this method produces more efficient estimates in terms of their variances compared to the estimates based on the current sample only. If these variance-covariance matrices are not known, their consistent estimates can be used as well such that the large sample properties of the method remain unchangeable. This approach allows to improve statistical properties of many standard estimators such as an empirical cumulative distribution function, empirical characteristic function, and Nelson-Aalen cumulative hazard estimator.


Mathematics Subject Classification. 62G05, 62G20

Key words: Auxiliary information, multiple data sources, partially grouped samples, convergence rates.


© EDP Sciences, SMAI 2006


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