Optimal Domain Estimation under Summation Restriction
Imbi Traat
University of Tartu,
Estonia
Date: Friday, November 09, 2007
Location: PSA 206
Time: 2:40pm
ABSTRACT:
The talk is based on the Ph.D. Thesis and on a joint
unpublished paper with Kaja Sõstra.
The users of official statistics usually require consistent
estimates. In domains' case the simplest requirement is that
estimated domain totals sum up to the estimated population
total. In fact, this relationship, naturally holding for the
true population parameters, is a kind of auxiliary information,
which should be incorporated into estimation process with the
aim to improve estimates.
Recently, Knottnerus (2003) has proposed a new estimator,
called General Restriction (GR) estimator that estimates a
parameter vector so that the restrictions are satisfied for the
estimates. The new estimator is optimal in the class of all
estimators satisfying the same restrictions and using the same
initial estimators in its construction.
Sõstra (2003) has developed these ideas for domain estimation
under summation restriction. Several good properties are
fulfilled for new domain estimators - they satisfy
restrictions, they are optimal, they are usually more precise
than the initial domain estimators.
In the presentation, the cases with estimated, fixed and
conditionally fixed population total are considered. The
restricted domain estimators are elaborated for initial ratio
estimators. It appears that the covariance structure of domain
ratio estimators is simple for some designs (the design-based
approach is used). Simple covariance structure of initial
estimators simplifies respective restriction estimators, so
that they can be easily calculated. In addition to the
formulae, illustrative simulation results under two sampling
designs are given.
References:
- Knottnerus, P. (2003). Sample Survey Theory: Some Pythagorean
Perspectives. New-York: Springer.
- Sõstra, K. (2007). Restriction Estimator for Domains. Ph.D.
Thesis, University of Tartu.
- Traat, I., Ilves, M. (2007). The Hypergeometric Sampling
design, Theory and Practice. Acta Appl Math 97(1-3), 311-321.
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