Dr. Gauri Sankar Datta - University of Georgia: Benchmarking Small Area Estimators

• Mon, 05/28/2012 - 3:00pm

Small area estimation has become a topic of growing importance in recent
years. Model-based small area estimates, when aggregated, need not correspond
to the direct survey estimate for a larger area, e.g., national, which may be
a cause of concern if (i) the sample size for the larger area is sufficiently
large that the direct estimate is regarded as  reliable, and/or (ii) the
direct estimate for the larger area has any sort of official status. 
Substantial deviation of  an aggregate of model-based small area estimates
from the corresponding direct estimate for a large area may also suggest
model failure. These considerations motivate benchmarking, which is some form
of calibration that adjusts individual area level estimates so they aggregate
to a direct estimate for a large area.   In this talk, we consider
benchmarking issues in the context of small area estimation. We find optimal
estimators within the class of benchmarked linear estimators under either
external or internal benchmark constraints. We extend existing results for
both external and internal benchmarking, and also provide some links between
the two. In addition, we obtain necessary and sufficient conditions for
self-benchmarking for an augmented model. Most of our results are found using
ideas of orthogonal projection.