A Method for Variance Estimation of Non-Linear Functions of Totals in Surveys – Theory and Software Implementation
Claes Andersson and Lennart Nordberg
This paper treats the estimation of standard errors in survey sampling. Let t^1, t^2,…,t^J be linear (e.g., Horvitz-Thompson) estimators of the population totals t1, t2,…,tJ. Simultaneous standard error estimation for a large number of functions fq(t^1, t^2,…t^J), q=1,2,…,Q, is a common problem at statistical agencies. Such estimation can be very demanding even for a mainframe computer as the number of totals is large and the totals are allowed to represent completely arbitrary population domains.
We present a technique which reduces this problem to a manageable form and yields asymptotically unbiased variance estimates. This technique, which is based on Taylor approximation and an extension of the Woodruff transformation method, has recently been implemented in a computer program developed at Statistics Sweden. This program, called CLAN, can handle arbitrary rational functions of domain and population totals and auxiliary information can easily be included. CLAN was written in the SAS language and works on PCs as well as mainframes.
Survey sampling; variance estimation; statistical software.