Post-stratification based on a choice of a randomization device (original) (raw)
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In this article, a combined general family of estimators is proposed for estimating finite population mean of a sensitive variable in stratified random sampling with non-sensitive auxiliary variable based on randomized response technique. Under stratified random sampling without replacement scheme, the expression of bias and mean square error (MSE) up to the first-order approximations are derived. Theoretical and empirical results through a simulation study show that the proposed class of estimators is more efficient than the existing estimators, i.e., usual stratified random sample mean estimator, Sousa et al (2014) ratio and regression estimator of the sensitive variable in stratified sampling.
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For various reasons individuals in a sample survey may prefer not to confide to the interviewer the correct answers to certain potentially sensitive questions such as the illegal use of drugs, illegal earning, or incidence of acts of domestic violence, etc. In such cases the individuals may elect not to reply at all or to reply with incorrect answers. The resulting evasive answer bias is ordinarily difficult to assess. The use of a randomized response method for estimating the proportion of individuals possessing those sensitive attributes can potentially eliminate the bias. Following Chaudhuri and Dihidar (2014) and Dihidar (2016), here, as a possible variant, we have made an attempt to estimate the sensitive population proportion using a combination of binomial and hypergeometric randomized responses by direct and inverse mechanism. Along with the traditional simple random sampling, with and without replacement, we consider here sampling of respondents by unequal probabilities. Essential theoretical derivations for unbiased estimator, variance and variance estimators are presented for several sampling schemes. A numerical illustration is performed to make a comparative study of the relative efficiencies of the direct and inverse mechanism.
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Sankhya B, 2014
We consider the problem of estimation of a finite population proportion (P) related to a sensitive character under the randomized response plans due to and Eriksson (1973) and prove that for a given probability sampling design, given any linear unbiased estimator (LUE) of P based on Warner's (1965) plan with any given value of the plan parameter there exists an LUE of P based on Eriksson's (1973) plan with a uniformly smaller variance for suitable choices of the plan parameters. The same is also shown to be true when the plan parameters for the two plans are so chosen so that both offer the same level of privacy.