A Dexterous Optional Randomized Response Model

Abstract

This article addresses the problem of estimating the proportion π S of the population belonging to a sensitive group using optional randomized response technique in stratified sampling based on Mangat model that has proportional and Neyman allocation and larger gain in efficiency. Numerically, it is found that the suggested model is more efficient than Kim and Warde stratified randomized response model and Mangat model.

An Improved Two-stage Stratified Randomized Response Model for Estimating Sensitive Proportion

“…The corrected results portray that Tarray et al (2017) estimator under Neyman allocation is approximately equally efficient compared to Mangat (1991; see Table 1). Further, the PRE of Tarray et al (2017) estimator under Neyman allocation and that of under proportional allocation remains also approximately equal (see Table 3). However, the PREs of Tarray et al (2017) with respect to Kim and Warde's (2004) estimator are encouraging.…”

“…We witnessed that there is a large gain in efficiency by using the Tarray et al (2017) estimator (under Neyman allocation) over to Kim and Warde's (2004) estimator pS (under Neyman allocation). The other findings by Tarray et al (2017) remain the same.…”

An alternative approach for construction of strata using quantified sensitivity level

“…Now we expand the minimal equation ( 16) in both sides using the relation expressed in (7) to ( 9) at common boundary points [x h ] for the h-th and i-th strata, then, it gives the approximate expression of the minimal equation of the variance. Using the relation ( 7), ( 8) and ( 9), the system of equations (16) giving optimum points of stratification can, therefore, be reduced into (17) where (18) (19) (20) Now proceeding on the lines of Singh and Sukhatme (1969) and using the relation expressed in (17), equivalently, the system of equations ( 16) can also be put as (21) Therefore, if we have a large number of strata so that the strata width are small and their higher powers in the expansion can be neglected, then the system of equations in (16) or equivalently the system of equations in (21) can be approximated as in view of the fact that is bounded for all x in (a, b). This method of finding the approximate optimum strata boundaries (AOSB) for Neyman allocation method shall be called the cumulative cube root rule denoted as cum.…”

“…Recently Singh and Gorey (2019) reviewed Gupta et al (2002) model by suggesting a modified optional randomized response model. For more detail, see further work which is done by Gjestvang and Singh (2006), Tarray et al (2015Tarray et al ( , 2017. Dalenius (1950) first introduced the methods for constructing optimum strata boundaries (OSB) when the study variable itself was used as a stratification variable.…”

A Remark on Gupta, Gupta and Singh Optional Randomized Response Model

“…through a randomization device. A rich growth of literature on randomized response techniques can be found in Tracy and Mangat (1996), Zou(1997), Singh and Joarder (1997), Singh (2001,2002), Singh and Mathur (2003), Gjestvang and Singh (2006), Singh and Tarray (2014), Tarray et al (2015), Tarray and Singh (2017). Eichhorn and Hayre (1983) proposed a scrambled randomized response method for estimating the mean µx and the variance 2 x  of the sensitive quantitative variable, say X.…”