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.