### U.S. Bureau of Labor Statistics

##
Office of Survey Methods Research

# Abstract

**Steve Woodruff** (1994) "One Way To
Build An Estimator, With Applications To Sampling Theory,"
Proceedings of the Section on Survey Research Methods, American
Statistical Association, forthcoming.

Although the random sampling distribution must be
considered when making inferences from sample survey data,
this distribution is rarely sufficient because of many
features of applied sampling. These features include
nonresponse, response bias, and data relationships that make
applied sampling a multivariate discipline where univariate
methods generally fail to produce optimal inferences. In
spite of this, sample survey inference has remained largely
univariate with an encyclopedia of corrective techniques to
handle these negative features of sample data. This paper
discusses theory and applications of multivariate methods for
estimating finite population mean vectors assuming data
deficiencies like nonresponse (both item and total, ignorable
and otherwise) and response bias, but exploiting data
dependencies modeled by the covariance matrix of survey
variables (both design and target variables). These data
dependencies are used to minimize mean square error in the
presence of the data deficiencies. The estimator so derived,
automatically handles many missing data problems that
practitioners face by fully exploiting known data
dependencies. Its use is indicated in repeated surveys where
nonresponse is a problem and strong data dependencies exist.
This methodology was developed for the Bureau's Current
Employment Statistics Survey but has applications in other
repeated surveys.

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**Last Modified Date: **March 2, 2016