Affiliations: Sampling and Official Statistics Unit, Indian Statistical Institute, Kolkata, India. E-mail: [email protected]
Abstract: In estimating the proportion of people bearing sensitive matters like habits
of tax evasion, drunken driving, etc.
in a given community, it is difficult to obtain trustworthy data through direct queries. To overcome this difficulty,
Warner [29] introduced randomized response techniques to estimate the proportion
of people bearing such a stigmatizing or sensitive characteristic in a given community.
Since then, several researchers
have extended and applied this technique in various ways, for instance, Greenberg et al. [13], Horvitz et al. [16], Mukerjee [23], Ljungqvist [20],
Christofides [10], Singh and Grewal [26], and many others. In many areas of the RR-related
activities, the sample selection is traditionally by simple random sampling (SRS) with
replacement (WR). Keeping in mind that the general large scale sample surveys usually involve the unequal probability sample selection, subsequently many researchers have enriched the RR-related literature by extending in unequal probability sampling (see Chaudhuri et al. [5], Dihidar [12], Chaudhuri and Dihidar [6]). Hanurav [14], Rao [25], Chaudhuri and Arnab [4] had compared some unequal probability sampling strategies for estimating the population mean of a quantitative variable in direct surveys under a super-population model.
In this paper, we consider the problem of estimating sensitive population proportion by unequal probability sampling using the pioneering randomized response techniques due to Warner [29], Mangat and Singh [22], Christofides [9], Chaudhuri and Mukerjee's [7] forced response model, Kuk's model [18], Singh and Joarder's [27] unknown repeated trial model and compare the Horvitz-Thompson's [17] and Murthy's [24] strategies under the super population model as proposed in Lanke [19]. It is shown that under this model-cum-design based approach, Murthy's strategy performs better than Horvitz-Thompson's strategy.
Keywords: Population proportion, unequal probability sampling, super population model, model-cum-design based approach
