Stochastic Randomized Response Model for a Quantitative Sensitive Random Variable

A new stochastic randomized response model is introduced that is useful for estimating the population mean of a sensitive quantitative variable. The proposed stochastic randomized response model is an extension of the stochastic randomized response model from a qualitative sensitive variable to a quantitative variable found in Singh (2002). The stochastic nature of a randomized response device helps increase a respondent’s cooperation while collecting information on sensitive variables in a society. The Bar-Lev, Bobovitch, and Boukai (2004) model is shown to be a special case of the proposed model

Sufficient bootstrapping

In this paper, we introduce an idea we refer to as sufficient bootstrapping, which is based on retaining only distinct individual responses, and also develop a theoretical framework for the techniques. We demonstrate through numerical illustrations that the proposed sufficient bootstrapping may be better than the conventional bootstrapping in certain situations. The expected gain by the sufficient bootstrapping has been computed for small and large sample sizes. The relative efficiency shows that there could be significant gain by the sufficient bootstrapping and it could reduce computational burden. Variance expressions for both the conventional and sufficient bootstrapping sample means are derived. Here the word "sufficient" is being used in the sense that it is "sufficient to take just one of any duplicated items in the bootstrap sample" and is not tightly connected to sufficiency in terms of any likelihood perspective. R code for comparing bootstrapping and sufficient bootstrapping are provided. A huge scope of further studies is suggested.Bootstrapping Sufficient bootstrapping Estimation of mean Resampling Distinct units

Cramer-Rao Lower Bound of Variance in Randomized Response Sampling

In this note, the Cramer-Rao lower bound of variance by using the two decks of cards in randomized response sampling has been developed. The lower bound of variance has been compared with the recent estimator proposed by Odumade and Singh at equal protection of respondents. A real practical face-to-face interview data collected using two decks of cards has been analyzed and the results are discussed.randomized response sampling; estimation of proportion; maximum likelihood estimation; relative efficiency

Estimation of Finite Population Variance Using Scrambled Responses in the Presence of Auxiliary Information

<div><p>In this article, a new estimator for estimating the finite population variance of a sensitive variable based on scrambled responses collected using a randomization device is introduced. The estimator is then improved by using known auxiliary information. The estimators due to Das and Tripathi (1978: Sankhya) and Isaki (1983: JASA) are shown to be special cases of the proposed estimator. Numerical simulations are performed to study the magnitude of the gain in efficiency when using the estimator with auxiliary information with respect to the estimator based only on the scrambled responses. An idea to extend the present work from SRSWOR design to more complex design is also given.</p></div

Calibrated estimators in two-stage sampling

<p>We consider the problem of the estimation of the population mean of a study variable by assuming that the population means of an auxiliary variable are known at both stages of sample selection. The design weights at the first and second stages of sample selection are calibrated by optimizing the chi-squared type distance between the design weights and the new weights at both the first and second stages of sample selection. The regression type estimator in two-stage sampling is shown to be a special case. An application of the proposed estimators using a real data set is discussed.</p

Post-stratification based on a choice of a randomization device

In this paper, we use the idea of post-stratification based on the respondents’ choice of a particular randomization device in order to estimate the population proportion of a sensitive characteristic. The proposed idea gives full freedom to the respondents and is expected to result in greater cooperation from them as well as to provide some increase in the relative efficiency of the newly proposed estimator

Estimation of population ratio, product, and mean using multiauxiliary information with random nonresponse

In this paper, a family of estimators of population ratio R , product P and mean Y0 has been suggested using multi-auxiliary information under simple random sampling without replacement (SRSWOR) and its properties have been discussed. We have further suggested three families of estimators in the presence of random non-response in different situations under an assumption that the number of sampling units on which information cannot be obtained due to random non-response follows some distribution. The estimators of the family involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error (MSE). The work of Singh et al. (2007) is shown as a special case. At the end, numerical comparisons are also made