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.

Classification : 62G05, 62G20

Mots clés : auxiliary information, multiple data sources, partially grouped samples, convergence rates

@article{PS_2006__10__11_0, author = {Tarima, Sergey and Pavlov, Dmitri}, title = {Using auxiliary information in statistical function estimation}, journal = {ESAIM: Probability and Statistics}, pages = {11--23}, publisher = {EDP-Sciences}, volume = {10}, year = {2006}, doi = {10.1051/ps:2005019}, zbl = {1136.62332}, mrnumber = {2188346}, language = {en}, url = {http://www.numdam.org/item/PS_2006__10__11_0/} }

Tarima, Sergey; Pavlov, Dmitri. Using auxiliary information in statistical function estimation. ESAIM: Probability and Statistics, Tome 10 (2006) , pp. 11-23. doi : 10.1051/ps:2005019. http://www.numdam.org/item/PS_2006__10__11_0/

[1] Estimating distribution functions from survey data. Biometrika 73 (1986) 597-604. | Zbl 0614.62005

and ,[2] Statistical estimation of probability distribution with auxiliary information [in Russian]. Tomsk State University, Tomsk (1988).

and ,[3] Counting processes and survival analysis. Wiley (1991). | MR 1100924 | Zbl 0727.62096

and ,[4] Minimum-contrast estimation taking into account additional information. J. Soviet Math. 53 (1991) 547-551.

and ,[5] Methods of weighting for unit non-response. The Statistician, Special Issue: Survey Design, Methodology and Analysis 40 (1991) 333-342.

and ,[6] Adjustment by minimum discriminant information. Ann. Statist. 12 (1984) 121-140. | Zbl 0583.62020

,[7] Median estimation in the presence of auxiliary information. J. R. Statist. Soc. B 51 (1989) 261-269. | Zbl 0674.62010

and ,[8] Contribution to the theory of estimation from grouped and partially grouped samples. Almqvist & Wiksell, Stockholm (1961). | MR 176560

,[9] Statistical analysis with missing data. Wiley (2002). | MR 1925014 | Zbl 1011.62004

and ,[10] Empirical likelihood. Chapman and Hall (2001). | Zbl 0989.62019

,[11] Mixed methods of determining probabilistic characteristics [in Russian]. Soviet Radio, Moscow (1973). | MR 429311

,[12] On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77 (1990) 365-375. | Zbl 0716.62013

, and ,[13] Confidence intervals for a distribution function in the presence of auxiliary information. Comput. Statist. Data Anal. 21 (1996) 327-342. | Zbl 0875.62136

,