Hostname: page-component-76d6cb85b7-6jg5l Total loading time: 0 Render date: 2026-07-13T11:57:10.639Z Has data issue: false hasContentIssue false
  • English
  • Français

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; starima@hpi.mcw.edu
Dmitri Pavlov
Affiliation:
Clinical Biostatistics, Pfizer Inc., 50 Pequot Avenue, New London, Connecticut, 06320, USA; dmitri.pavlov@pfizer.com
Get access

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.

Information

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

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.)

Article purchase

Temporarily unavailable

References

Chambers, R.L. and Dunstan, R., Estimating distribution functions from survey data. Biometrika 73 (1986) 597–604. CrossRef
Y.G. Dmitriev and Y.C. Ustinov, Statistical estimation of probability distribution with auxiliary information [in Russian]. Tomsk State University, Tomsk (1988).
T.R. Fleming and D.P. Harrington, Counting processes and survival analysis. Wiley (1991).
Gal'chenko, M.V. and Gurevich, V.A., Minimum-contrast estimation taking into account additional information. J. Soviet Math. 53 (1991) 547–551. CrossRef
D. Holt and D. Elliot, Methods of weighting for unit non-response. The Statistician, Special Issue: Survey Design, Methodology and Analysis 40 (1991) 333–342.
Haberman, S.J., Adjustment by minimum discriminant information. Ann. Statist. 12 (1984) 121–140. CrossRef
Kuk, A.Y.C. and Mak, T.K., Median estimation in the presence of auxiliary information. J. R. Statist. Soc. B 51 (1989) 261–269.
G. Kulldorff, Contribution to the theory of estimation from grouped and partially grouped samples. Almqvist & Wiksell, Stockholm (1961).
R.J.A. Little and D.B. Rubin, Statistical analysis with missing data. Wiley (2002).
A.B. Owen, Empirical likelihood. Chapman and Hall (2001).
V.N. Pugachev, Mixed methods of determining probabilistic characteristics [in Russian]. Soviet Radio, Moscow (1973).
Rao, J.N.K., Kovar, J.G. and Mantel, H.J., On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77 (1990) 365–375. CrossRef
Zhang, B., Confidence intervals for a distribution function in the presence of auxiliary information. Comput. Statist. Data Anal. 21 (1996) 327–342. CrossRef