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Estimation of a finite population variance under linear models for randomized response designs. (English) Zbl 1365.62040
Chaudhuri, Arijit (ed.) et al., Data gathering, analysis and protection of privacy through randomized response techniques: qualitative and quantitative human traits. Amsterdam: Elsevier/North Holland (ISBN 978-0-444-63570-9/hbk; 978-0-444-63571-6/ebook). Handbook of Statistics 34, 221-231 (2016).
Summary: Considering a linear model which combines random permutation model and models applicable to a wide class of randomized response (RR) designs, as developed by D. R. Bellhouse [J. Am. Stat. Assoc. 75, 1001–1004 (1980; Zbl 0456.62012)], we have examined here the problem of finding optimal sampling strategies for estimating a finite population variance. An optimal estimator with a constant variance has been obtained within the class of all nonhomogeneous quadratic design-model-unbiased (model-unbiased) estimators of population variance, for any fixed-size noninformative sampling design. For the class of sampling designs including srswor, the same estimator remains optimal within the class of all quadratic design unbiased estimators for a particular case of the assumed random permutation model. In case the random permutation assumption is dropped, it is proved that there does not exist any uniformly minimum variance estimator in the entire class of design model unbiased estimators. Under certain conditions and under a slightly different RR model a uniformly minimum variance unbiased estimator has been obtained.
For the entire collection see [Zbl 1349.62001].
62D05 Sampling theory, sample surveys
62J05 Linear regression; mixed models
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