Mean and sensitivity estimation of a sensitive variable through additive scrambling

Abstract

This article focuses on reducing the additional variance due to randomization of the responses. The idea of additive scrambling and its inverse has been used along with (i) split sample approach and (ii) double response approach. Specifically, our proposal is based on Gupta et al. (2006) randomized response model. We selected this model for improvement because it provides estimator of mean and sensitivity level of a sensitive variable and is better than all of its competitors proposed earlier to it and even Gupta et al. (2006) sensitivity estimator is better than that of Gupta et al. (2010). Our suggested estimators are unbiased estimators and perform better than Gupta et al. (2006) estimator. The issue of privacy protection is also discussed.     

Optimal designing of an SkSP-R double sampling plan

In this article, we propose a method of planning and determining the optimum parameters of a SkSP-R skip-lot sampling plan by using the attribute double sampling plan as the reference plan. The SkSP-R plan is a new type of skip-lot sampling plan which has a provision for re-inspecting the submitted lots. The optimal plan parameters of the suggested sampling plan are estimated with the target that the average sample number be minimized and satisfying both the specified producer's as well as the consumer's risks simultaneously. In order to obtain the optimum parameters, tables are also built for different combinations of the acceptable quality level and the limiting quality level in conjunctions with different producer's and consumer's risks. An illustrative example is provided for the implementation of the suggested plan. The advantages of the suggested plan over the existing conventional sampling plans and other existing skip-lot sampling plans are also described.     

On using non identical and independent Bernoulli trials in human surveys

Unlike the usual randomized response techniques, as a pioneering attempt, this article focuses on using non identical independent Bernoulli trials in sensitive surveys. For this purpose, a general class of randomized response techniques is considered. The usual randomized response techniques are based on a fixed probability of having a yes answer. Contrary to usual techniques, in the proposed technique every respondent has a different probability of reporting a yes answer. With this setting, in most of the situations, the proposed technique is observed performing better in terms of variability. To illustrate and support the superiority of the proposed technique it is compared with models such as Warner (1965), Greenberg et al. (1969), Mangat and Singh (1990), and Mangat (1994) using identical Bernoulli trials. Relative efficiency and privacy protection are studied in detail using Warner (1965) and Mangat (1994) models.     

Demand shocks and employment adjustments: Does employment protection legislation create rigidity?

With state‐level panel data from the Indian manufacturing sector for 2000–12, and labour turnover as a proxy for employment adjustments, the authors estimate differential effects of demand shocks on employment adjustment across states with high and low levels of EPL. They find that EPL does not hinder employment adjustment; the response of labour separation rates to negative demand shocks is relatively higher in states with high levels of EPL, and labour turnover is inversely associated with EPL, which may be viewed as indicative of the beneficial effects of EPL for both enterprises and workers.     

Ribā-Based Mortgages in Dār al-Harb: An Issue of Modernist Application of Fiqh al-Aqalliyāt for Muslim Minorities

The growing presence of Muslims in the occident living as minorities in majority non-Muslim countries comes with inherent religious challenges. How can occidental Muslims live faithfully in cultures that cause perceivable “hardship” without compromising their religio-legal obligations? Is fiqh al-aqalliyāt the answer to this problem, if at all there is a problem? As a sample of the so-called “hardship”, this paper looks at the issue of occidental Muslims taking out ribā (interest or usury) based loans in order to buy a house, to test the theory of whether or not a new legal doctrine is required to facilitate Muslim needs facing exceptional circumstances. Is it a clash between classical and contemporary scholarship or an inevitable pre-modern evolution of Islamic jurisprudence? This article argues that juristic opinions, whether classical or contemporary do not justify any actions, because their opinions are first and foremost non-binding and secondly a result of their endeavor to come to an edict. The paper highlights a misapplication of juristic maxims and opinions, driven by zeal to provide an edict to justify the needs of some. It concludes that no added value is made to Islamic law by heterodox jurisprudence.     

Design of acceptance sampling plan using a modified EWMA statistic

In this paper, a modified exponentially weighted moving average (EWMA) statistic is proposed. The approximate distribution of the proposed modified EWMA statistic is derived. A variable acceptance sampling plan is designed using the proposed EWMA statistic. The plan parameters of the proposed sampling plan are determined such that the given producer's risk and consumer's risk are satisfied. The efficiency of the proposed plan based on the new EWMA statistic is compared with the existing EWMA plan in terms of the sample size required. The application of the proposed plan is given with the help of an example.     

Progressive Variance Control Charts for Monitoring Process Dispersion

In a process, the deviation from location or scale parameters affects the quality of the process and waste resources. So it is essential to monitor such processes for possible changes due to any assignable causes. Control charts are the most famous tool used to meet this intention. It is useless to monitor process location until the assurance that process dispersion is in-control. This study proposes some new two-sided memory control charts named as progressive variance (PV) control charts which are based on sample variance to monitor changes in process dispersion assuming normality of quality characteristic to be monitored. Simulation studies are made, and an example is discussed to evaluate the performance of the proposed charts. The comparison of the proposed chart is made with exponentially weighted moving average- and cumulative sum-type charts for process dispersion. The study shows that performance of the proposed charts are uniformly better than its competitors for detecting positive shifts while for detecting negative shift in the variance their performance is better for small shifts and reasonably good for moderated shifts.     

On Optimum Regression Estimator for Population Mean Using Two Auxiliary Variables in Simple Random Sampling

In this paper, a difference-in-regression estimator is proposed by using two auxiliary variables in simple random sampling. Variance of proposed estimator up to the first order of approximation is compared with other competing estimators. Additionally, by taking the known value of one of the population regression coefficients, another version of the proposed estimator is also obtained. The proposed estimator is found optimum in the class of estimators based on two auxiliary variables. A simulation study is carried out in support with theoretical results. If only the means of auxiliary variables are available, another estimator can be obtained for large trivariate normal population.     

On Using Negative Binomial Distribution as a Randomization Device in Sensitive Surveys

In this article, an interesting improvement of some recent randomized response techniques has been proposed. The proposed randomized response technique applies Negative Binomial distribution to obtain data from respondents. An unbiased estimator of proportion of a sensitive attribute has been suggested and it is shown, numerically, that the new estimator performs better than the recent estimators while doing a sensitive survey. It is also established that the proposed estimator is unconditionally better than that of the estimator based on using the geometric distribution.