ON MEASURES OF UNCERTAINTY OF EMPIRICAL BAYES SMALL-AREA ESTIMATORS
Partha Lahiri
University of Nebraska-Lincoln
Refreshments: 3:30 - 4:00 p.m. Monday, November 1, at 327 Yost Talk: 4:00 - 5:00 p.m. Monday, November 1, at 327 Yost.
Small-area typically refers to a small geographic area or a demographic
group for which very little information is obtained from the sample surveys.
An empirical Bayes method uses sample survey data in conjunction with relevant
supplementary data which are obtained from various administrative sources.
The method has been found to be very useful in many applications of
small-area estimation and related problems.
A method based on bootstrap samples is proposed to measure the accuracy of
the proposed empirical Bayes estimator of a small-area characteristic.
A simple approximation of the method which does not require any bootstrap
simulation is also proposed. The model expectation of the proposed measure
of uncertainty of the empirical Bayes (EB) estimator is equal to the
integrated
Bayes risk of the EB estimator up to the order $o(m^{-1}),$ where $m$ denotes
the number of small-areas. It is interesting to note that for a special case
of our model, the measure is identical, up to the order $o(m^{-1})$, with a
measure of uncertainty previously proposed by Morris (1983). Since Morris'
measure
is an approximation to a hierarchical Bayes posterior variance, the proposed
method enjoys both desirable frequentist and hierarchical Bayes properties.
Two well-known data sets are considered to compare the proposed method with
some
existing methods. A Monte Carlo simulation is conducted to compare the
performances
of different measures of uncertainty.
(This is a joint work with Ferry Butar Butar, Sam Houston State University)
Questions? Nidhan Choudhuri