Variance Estimation in Randomized Response Surveys
Document Type
Book Chapter
Publication Title
Handbook of Statistics
Abstract
Warner (1965) pioneered the randomized response technique to collect information on a sensitive qualitative character. Following Adhikary (2013) we propose a straightforward procedure to derive an exact expression for the variance of a homogeneous linear unbiased estimator of a population total of a sensitive quantitative character such as expenditure on drinking alcohol, additional income earned over usual salary to hide income tax in the income tax return, expenditure on gambling, number of induced abortions, income earned through prostitution, expenditure incurred toward payment of prostitutes in a red light area, and some such others which we do not want to disclose even to our wives. Following Adhikary (2013) an attempt has been made to derive an unbiased estimator of the variance of the estimator. This procedure is illustrated with Horvitz-Thompson (1952) estimator, Hansen-Hurwitz (1943) estimator based on probability proportional to size with replacement (PPSWR) sampling and also an improved version of it obtained by Rao-Blackwellization as considered by Adhikary (2009a,b), Raj's (1956) ordered estimator and Murthy's (1957) unordered estimator both based on PPSWOR sampling, ratio estimator based on Lahiri (1951), Midzuno (1952), and Sen's (1953) sampling scheme, and Hartley-Ross's (1954) unbiased ratio-type estimator based on SRSWOR sampling scheme considering in each case the form of the estimator suitable for the randomized response survey.
First Page
191
Last Page
208
DOI
10.1016/bs.host.2016.01.010
Publication Date
1-1-2016
Recommended Citation
Adhikary, A. K., "Variance Estimation in Randomized Response Surveys" (2016). Book Chapters. 257.
https://digitalcommons.isical.ac.in/book-chapters/257
