Estimation of a Finite Population Variance Under Linear Models for Randomized Response Designs
Document Type
Book Chapter
Publication Title
Handbook of Statistics
Abstract
Considering a linear model which combines random permutation model and models applicable to a wide class of randomized response (RR) designs, as developed by Bellhouse (1980), 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.
First Page
221
Last Page
231
DOI
10.1016/bs.host.2016.01.012
Publication Date
1-1-2016
Recommended Citation
Mukhopadhyay, P., "Estimation of a Finite Population Variance Under Linear Models for Randomized Response Designs" (2016). Book Chapters. 231.
https://digitalcommons.isical.ac.in/book-chapters/231
