Naurang Singh Mangat

Some alternative strategies to Moors’ model in randomized response sampling

Abstract In this paper, it is shown that the optimality condition advocated by Moors (1971, J. Amer. Statist. Assoc. 66, 627–629) for Greenberg et al. (1969, J. Amer. Statist. Assoc. 64, 520–539) randomized response (RR) model is not desirable in the sense that it jeopardizes the privacy of response for a group of respondents which is against the main objective of RR survey technique. Two modifications of Moors’ model are proposed which do not suffer from the above serious drawback. An empirical investigation has also been carried out to examine the relative efficiency aspect of one of the two proposed strategies.

An Improved Unrelated Question Randomized Response Strategy

We consider the problem of estimating π the proportion of human population belonging to the sensitive category. A new randomized response procedure using known πr (the proportion of population possessing a non-stigmatized attribute) bas been proposed. The proposed strategy provides unbiased and more efficient estimator of π than the one based on Greenberg et al.s (1969) usual unrelated question randomized response model with known πr

An improved two stage randomized response strategy

Mangat and Singh (1990) have suggested a two stage randomized response technique to estimate the proportion of population possessing a sensitive attribute. The procedure was shown to be more efficient than the procedure due to Warner (1965). Recently, Tracy and Osahan (1993) have suggested a modification to the Mangat and Singh (1990) procedure which results in a more efficient strategy in practice. In this paper we propose a modification to the Tracy and Osahan (1993) procedure. The modified procedure is a generalization of Tracy and Osahan (1993) and is always more efficient than their strategy. An empirical study has also been undertaken to find the extent of relative efficiency.

A mail survey design for sensitive character without using randomization device

In the present study, we develop theory for Takahasi and Sakasegawas (1977) suggest ion and propose a new randomized response model suitable for mail surveys. The proposed model based estimator is unbiased and is always more efficient than the estimator based on Takahasi and Sakasegawa model.

Simple Random Sampling

Simple Random Sampling (SRS) is the simplest and most common method of selecting a sample, in which the sample is selected unit by unit, with equal probability of selection for each unit at each draw. In other words, simple random sampling is a method of selecting a sample s of n units from a population Ω of size N by giving equal probability of selection to all units. It is a sampling scheme in which all possible combinations of n units may be formed from the population of N units with the same chance of selection.

Regression Method of Estimation

Analogous to the ratio and product estimators, the linear regression estimator is also designed to increase the efficiency of estimation by using information on the auxiliary variable x which is correlated with the study variable y. As stated before, the ratio method of estimation is at its best when the correlation between y and x is positive and high, and also the regression of y on x is linear through the origin. In practice, however, it is observed that even when the regression of y on x is linear, the regression line passes through a point away from the origin. The efficiency of the ratio estimator in such cases is very low, as it decreases with the increase in length of the intercept cut on y-axis by the regression line. Regression estimator is the appropriate estimator for such situations. Although this estimator requires little more calculations than the ratio estimator, it is always at least as efficient as the ratio estimator for estimating population mean or total. Similarly, the product estimator of population mean or total is never more efficient than the corresponding linear regression estimator.

On respondent's jeopardy in two alternate questions randomized response model

This paper brings to light the situations where the two alternate questions randomized response model proposed by Folsom et al. (1973) is incapable of protecting the privacy of the respondent. A modification to achieve this is proposed so that the privacy of the respondent is protected in all the situations. The estimator based on the proposed modifications is always more efficient than Tracy and Mangats (1995) estimator and the usual estimator proposed by Horvitz et al. (1967) and Greenberg et al. (1969).

Collection of Survey Data

The need to gather information arises in almost every conceivable sphere of human activity. Many of the questions that are subject to common conversation and controversy require numerical data for their resolution. Data resulting from the physical, chemical, and biological experiments in the form of observations are used to test different theories and hypotheses. Various social and economic investigations are carried out through the use and analysis of relevant data. The data collected and analyzed in an objective manner and presented suitably serve as basis for taking policy decisions in different fields of daily life.

Sampling from Mobile Populations

The estimation of size is of immense importance in a variety of mobile biological populations. It helps to study population growth, ecological adaptation, natural selection, evolution, maintenance of many wildlife populations, and so on. Unlike other populations considered in previous chapters, the sampling units in the wildlife populations do not remain fixed at one place. They are rather highly mobile. Therefore, for mobile populations, it is essential to use alternative approach for sampling and estimation.

Two-Phase Sampling

The discussion in some of the previous chapters has revealed that the prior information on an auxiliary variable could be used to enhance the precision of an estimator. Ratio, product, and regression estimators require the knowledge of population mean \( \bar X \) (or equivalently of total X) for the auxiliary variable x. For stratifying the population on the basis of the auxiliary variable, knowledge of its frequency distribution is required.