# Using auxiliary information in statistical function estimation

ESAIM: Probability and Statistics (2005)

- Volume: 10, page 11-23
- ISSN: 1292-8100

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topTarima, Sergey, and Pavlov, Dmitri. "Using auxiliary information in statistical function estimation." ESAIM: Probability and Statistics 10 (2005): 11-23. <http://eudml.org/doc/104344>.

@article{Tarima2005,

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.
},

author = {Tarima, Sergey, Pavlov, Dmitri},

journal = {ESAIM: Probability and Statistics},

keywords = {Auxiliary information; multiple data sources; partially
grouped samples; convergence rates.; partially grouped samples; convergence rates},

language = {eng},

month = {12},

pages = {11-23},

publisher = {EDP Sciences},

title = {Using auxiliary information in statistical function estimation},

url = {http://eudml.org/doc/104344},

volume = {10},

year = {2005},

}

TY - JOUR

AU - Tarima, Sergey

AU - Pavlov, Dmitri

TI - Using auxiliary information in statistical function estimation

JO - ESAIM: Probability and Statistics

DA - 2005/12//

PB - EDP Sciences

VL - 10

SP - 11

EP - 23

AB -
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.

LA - eng

KW - Auxiliary information; multiple data sources; partially
grouped samples; convergence rates.; partially grouped samples; convergence rates

UR - http://eudml.org/doc/104344

ER -

## References

top- R.L. Chambers and R. Dunstan, Estimating distribution functions from survey data. Biometrika73 (1986) 597–604. Zbl0614.62005
- Y.G. Dmitriev and Y.C. Ustinov, Statistical estimation of probability distribution with auxiliary information [in Russian]. Tomsk State University, Tomsk (1988). Zbl0682.62001
- T.R. Fleming and D.P. Harrington, Counting processes and survival analysis. Wiley (1991). Zbl0727.62096
- M.V. Gal'chenko and V.A. Gurevich, Minimum-contrast estimation taking into account additional information. J. Soviet Math.53 (1991) 547–551.
- D. Holt and D. Elliot, Methods of weighting for unit non-response. The Statistician, Special Issue: Survey Design, Methodology and Analysis40 (1991) 333–342.
- S.J. Haberman, Adjustment by minimum discriminant information. Ann. Statist.12 (1984) 121–140. Zbl0583.62020
- A.Y.C. Kuk and T.K. Mak, Median estimation in the presence of auxiliary information. J. R. Statist. Soc. B51 (1989) 261–269. Zbl0674.62010
- 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). Zbl1011.62004
- A.B. Owen, Empirical likelihood. Chapman and Hall (2001). Zbl0989.62019
- V.N. Pugachev, Mixed methods of determining probabilistic characteristics [in Russian]. Soviet Radio, Moscow (1973).
- J.N.K. Rao, J.G. Kovar and H.J. Mantel, On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika77 (1990) 365–375. Zbl0716.62013
- B. Zhang, Confidence intervals for a distribution function in the presence of auxiliary information. Comput. Statist. Data Anal.21 (1996) 327–342. Zbl0875.62136

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