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Using auxiliary information in statistical function estimation

Published online by Cambridge University Press:  16 December 2005

Sergey Tarima  and
Dmitri Pavlov
Sergey Tarima
Affiliation:
Division of Biostatistics, Medical College of Wisconsin, 8701 Watertown Plank Road, Milwaukee, Wisconsin, 53226, USA; [email protected]
Dmitri Pavlov
Affiliation:
Clinical Biostatistics, Pfizer Inc., 50 Pequot Avenue, New London, Connecticut, 06320, USA; [email protected]
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Abstract

In many practical situations sample sizes are not sufficiently largeand estimators based on such samples may not be satisfactory interms of their variances. At the same time it is not unusual thatsome auxiliary information about the parameters of interest isavailable. This paper considers a method of using auxiliaryinformation for improving properties of the estimators based on acurrent sample only. In particular, it is assumed that theinformation is available as a number of estimates based on samplesobtained from some other mutually independent data sources. Thismethod uses the fact that there is a correlation effect betweenestimators based on the current sample and auxiliary informationfrom other sources. If variance covariance matrices of vectors ofestimators used in the estimating procedure are known, this methodproduces more efficient estimates in terms of their variancescompared to the estimates based on the current sample only. If thesevariance-covariance matrices are not known, their consistentestimates can be used as well such that the large sample propertiesof the method remain unchangeable. This approach allows to improvestatistical properties of many standard estimators such as anempirical cumulative distribution function, empirical characteristicfunction, and Nelson-Aalen cumulative hazard estimator.

Keywords

Auxiliary informationmultiple data sourcespartiallygrouped samplesconvergence rates.
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 10 , February 2006 , pp. 11 - 23
Copyright
© EDP Sciences, SMAI, 2006

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