Exact linear unbiased estimation in survey sampling
Exact linear unbiased estimation in survey sampling
The concept of the linearity of estimators in finite population inference is not well defined. We propose that linearity should be defined for both estimators and estimands and that strict linearity should be related constructively to the property of unbiasedness. We establish the conditions for the class of general linear estimators, introduced by Godambe (J. Roy. Statist. Soc. 17 (1955) 269), to be strictly linear. The ideas are extended to quadratic estimators of quadratic estimands. The implications are explored for ratio estimators, and domains of study, the latter extendible to poststratification.
linear estimator, strictly linear, linear estimand, quadratic estimand, unbiasedness, ratio estimator, domain
25-45
Sugden, R.A.
0483483b-5c6c-4f41-9b21-ff25a1c0e4ac
Smith, T.M.F.
61602253-c2d6-43a1-862b-291379e75318
1 March 2002
Sugden, R.A.
0483483b-5c6c-4f41-9b21-ff25a1c0e4ac
Smith, T.M.F.
61602253-c2d6-43a1-862b-291379e75318
Sugden, R.A. and Smith, T.M.F.
(2002)
Exact linear unbiased estimation in survey sampling.
Journal of Statistical Planning and Inference, 102 (1), .
(doi:10.1016/S0378-3758(00)00325-6).
Abstract
The concept of the linearity of estimators in finite population inference is not well defined. We propose that linearity should be defined for both estimators and estimands and that strict linearity should be related constructively to the property of unbiasedness. We establish the conditions for the class of general linear estimators, introduced by Godambe (J. Roy. Statist. Soc. 17 (1955) 269), to be strictly linear. The ideas are extended to quadratic estimators of quadratic estimands. The implications are explored for ratio estimators, and domains of study, the latter extendible to poststratification.
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Published date: 1 March 2002
Keywords:
linear estimator, strictly linear, linear estimand, quadratic estimand, unbiasedness, ratio estimator, domain
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Statistics
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Local EPrints ID: 30036
URI: http://eprints.soton.ac.uk/id/eprint/30036
ISSN: 0378-3758
PURE UUID: bab944e5-6ab3-4828-82bb-2c3cc329f8fe
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Date deposited: 11 May 2006
Last modified: 15 Mar 2024 07:36
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Author:
R.A. Sugden
Author:
T.M.F. Smith
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