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.
Keywords: 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}, mrnumber = {2188346}, zbl = {1136.62332}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps:2005019/} }
TY - JOUR AU - Tarima, Sergey AU - Pavlov, Dmitri TI - Using auxiliary information in statistical function estimation JO - ESAIM: Probability and Statistics PY - 2006 SP - 11 EP - 23 VL - 10 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps:2005019/ DO - 10.1051/ps:2005019 LA - en ID - PS_2006__10__11_0 ER -
Tarima, Sergey; Pavlov, Dmitri. Using auxiliary information in statistical function estimation. ESAIM: Probability and Statistics, Volume 10 (2006), pp. 11-23. doi : 10.1051/ps:2005019. http://www.numdam.org/articles/10.1051/ps:2005019/
[1] Estimating distribution functions from survey data. Biometrika 73 (1986) 597-604. | Zbl
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 | Zbl
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
,[7] Median estimation in the presence of auxiliary information. J. R. Statist. Soc. B 51 (1989) 261-269. | Zbl
and ,[8] Contribution to the theory of estimation from grouped and partially grouped samples. Almqvist & Wiksell, Stockholm (1961). | MR
,[9] Statistical analysis with missing data. Wiley (2002). | MR | Zbl
and ,[10] Empirical likelihood. Chapman and Hall (2001). | Zbl
,[11] Mixed methods of determining probabilistic characteristics [in Russian]. Soviet Radio, Moscow (1973). | MR
,[12] On estimating distribution functions and quantiles from survey data using auxiliary information. Biometrika 77 (1990) 365-375. | Zbl
, and ,[13] Confidence intervals for a distribution function in the presence of auxiliary information. Comput. Statist. Data Anal. 21 (1996) 327-342. | Zbl
,Cited by Sources: