  The U.S. Bureau of Labor Statistics use monthly, by-state employment totals
from the Current Population Survey (CPS) as a key input to develop employment
estimates for counties within the states. The monthly CPS by-state totals,
however, express high levels of volatility that compromise the accuracy of
resulting estimates composed for the counties. Typically-employed models for
small area estimation produce de-noised, state-level employment estimates by
borrowing information over the survey months, but assume independence among the
collection of by-state time series, which is typically violated due to
similarities in their underlying economies. We construct Gaussian process and
Gaussian Markov random field alternative functional prior specifications, each
in a mixture of multivariate Gaussian distributions with a Dirichlet process
(DP) mixing measure over the parameters of their covariance or precision
matrices. Our DP mixture of functions models allow the data to simultaneously
estimate a dependence among the months and between states. A feature of our
models is that those functions assigned to the same cluster are drawn from a
distribution with the same covariance parameters, so that they are similar, but
don't have to be identical. We compare the performances of our two alternatives
on synthetic data and apply them to recover de-noised, by-state CPS employment
totals for data from $2000-2013$.
