  Variance estimation for estimators of state, county, and school district
quantities derived from the Census 2000 long form are discussed. The variance
estimator must account for (1) uncertainty due to imputation, and (2) raking to
census population controls. An imputation procedure that imputes more than one
value for each missing item using donors that are neighbors is described and
the procedure using two nearest neighbors is applied to the Census long form.
The Kim and Fuller [Biometrika 91 (2004) 559--578] method for variance
estimation under fractional hot deck imputation is adapted for application to
the long form data. Numerical results from the 2000 long form data are
presented.
