Considerations and Results on Fay-Train Variance Replication

Thomas M. Menino Convention & Exhibition Center 

Fay-Train replication guides many of the U.S. Census Bureau's variance estimation practices, particularly for the American Community Survey (ACS) and the Current Population Survey (CPS). The replication method begins by internally linearizing a positive semi-definite quadratic form used to represent the variance structure of a total estimator. This linearization produces a set of replication factors which, when differenced against survey weights and squared, recover the original quadratic form and, thus, the total's variance. This form of replication factor is subsequently used to construct variance estimators for non-linear functions, as well as both linear and non-linear variance estimators under raking and calibration constraints. This paper examines the vector and matrix forms of Fay-Train replication, clarifies its use and common misconceptions, discusses the properties of Fay-Train when the discrepancy between replication weights and survey weights are arbitrarily small, and briefly introduces related accumulated and ongoing research.

replication methods

survey variance estimation

Fay-Train linearization

official statistics

weight calibration

American Community Survey (ACS) 

Survey Research Methods Section