On estimating the proportion of a qualitative sensitive character using randomized response sampling

In this paper, we present results pertaining to investigations concerning randomized response sampling. We consider a simple generalization for some existing investigations, and then provide the suitable choices for design parameters. It is also demonstrated the superiority of the proposed procedure over Warner (1965) procedure.     

Estimation of the mean in ranked set sampling with non responses

The estimation of the population mean when ranked set sampling [rss] is used for selecting the sample and non responses [nr] are present, is studied. The nr stratum is sub sampled using simple random sampling with replacement. Two strategies are analyzed. One of them is based on the selection of a sub sample from the nr in each cycle. The other uses sub samples selected among the nr in each rank.  The accuracy of the proposed estimators is characterized by the corresponding expected variances. Simulations and real life data are used for analyzing the behavior of them. Acknowledgements: This paper was developed partially during the visit of the author to Université des Antilles et Gouyane. The author gratefully acknowledges the helpful suggestions of the referees and thanks the support of DAAD for visiting Humboldt University where a version of the paper version was made.     

Estimation for sensitive characteristics using optional randomized response technique

This paper considers the problem of procuring honest responses to estimate the population mean of sensitive quantitative characteristics. It aims at pointing out that potential difference between sub-populations seems to be unnoticed under the usual optional randomized response technique. To make an extension to cover all the situations, we propose two alternative survey procedures that enable us to estimate the mean and the variance unbiasedly. Estimation for the sensitivity level of a question is under consideration as well. Efficiency comparisons have also been carried out to study the performances of the proposed procedures.     

Forced quantitative randomized response model: a new device

In the present investigation, a new forced quantitative randomized response (FQRR) model has been proposed. Both situations when the values of the forced quantitative response are known and unknown are studied. The forced qualitative randomized response models due to Liu and Chow (J Am Stat Assoc 71:72–73, 1976a, Biometrics 32:607–618, 1976b) and Stem and Steinhorst (J Am Stat Assoc 79:555–564, 1984) are shown as a special case of the situation when the value of the forced quantitative randomized response is simply replaced by a forced “yes” response. The proposed FQRR model remains more efficient than the recent Bar-Lev et al. (Metrika, 60:255–260, 2004), say BBB model. The relative efficiency of the proposed FQRR model with respect to the existing competitors, like the BBB model, has been investigated under different situations. No doubt the present model will lead to several new developments in the field of randomized response sampling. The proposed FQRR model will encourage researchers/scientists to think more on these lines.     

A note on randomized response models for quantitative data

Standard randomized response (RR) models deal primarily with surveys which usually require a yes or a no response to a sensitive question, or a choice for responses from a set of nominal categories. As opposed to that, Eichhorn and Hayre (1983) have considered survey models involving a quantitative response variable and proposed an RR technique for it. Such models are very useful in studies involving a measured response variable which is highly sensitive in its nature. Eichhorn and Hayre obtained an unbiased estimate for the expectation of the quantitative response variable of interest. In this note we propose a procedure which uses a design parameter (controlled by the experimenter) that generalizes Eichhorn and Hayres results. Such a procedure yields an estimate for the desired expectation which has a uniformly smaller variance.Acknowledgements We are grateful to two referees for their valuable and constructive comments.     

Unbiased estimators of mean, variance and sensitivity level for quantitative characteristics in finite population sampling

This paper considers the problem of procuring reliable information on sensitive quantitative characteristics without exposing respondents’ identities. A generalized optional randomized response procedure is proposed, which enables us to estimate some unknown population parameters unbiasedly. In particular, conditions for the assurance of unbiased estimations of mean, variance and sensitivity level are studied. Efficiency comparisons are also carried out to study the performance of the proposed procedure.     

Bayesian estimation of proportion and sensitivity level in randomized response procedures

A Bayesian approach to the joint estimation of population proportion and sensitivity level of a stigmatizing attribute is proposed by adopting a two-stage randomized response procedure. In the first stage the direct question method is carried out for each respondent, while in the second stage the randomization is exclusively carried out for those individuals declaring their membership in the non-sensitive group. The randomization is implemented on the basis of Franklin’s procedure. The proposed Bayesian method avoids the drawbacks usually connected with the use of maximum-likelihood or moment estimation.     

Estimation of population proportion in randomized response sampling using weighted confidence interval construction

This paper considers the problem of estimation for binomial proportions of sensitive attributes in the population of interest. Randomized response techniques are suggested for protecting the privacy of respondents and reducing the response bias while eliciting information on sensitive attributes. By applying the Wilson (J Am Stat Assoc 22:209–212, 1927) score approach for constructing confidence intervals, various probable point estimators and confidence interval estimators are suggested for the common structures of randomized response procedures. In addition, efficiency comparisons are carried out to study the performances of the proposed estimators for both the cases of direct response surveys and randomized response surveys. Circumstances under which each proposed estimators is better are also identified.     

A general class of estimators for estimating population mean using auxiliary information

Summary A general class of estimators for estimating the population mean of the character under study which make use of auxiliary information is proposed. Under simple random sampling without replacement (SRSWOR), the expressions of Bias and Mean Square Error (MSE), up to the first and the second degrees of approximation are derived. General conditions, up to the first order approximation, are also obtained under which any member of this class performs more efficiently than the mean per unit estimator, the ratio estimator and the product estimator. The class of estimators in its optimum case, under the first degree approximation, is discussed. It is shown that it is not possible to obtain optimum values of parameters “a”, “b” and “p”, that are independent of each other. However, the optimum relation among them is given by (b−a)p=ρ C _y/C _x. Under this condition, the expression of MSE of the class is that of the linear regression estimator.     

Alternative procedures for converting qualitative response data to quantitative expectations: An application to Australian manufacturing

This paper analyses and extends alternative procedures for converting qualitative expectations responses to quantitative expectations. A number of conversion procedures is investigated, including the probability model, the time-varying parameter probability model, and the regression approach. The informational content of the survey expectations is compared with simple time series models. It is found that the expectations models are superior for many series, both in terms of producing lower forecast root mean square error (RMSE) values and in detecting turning points in the actual data. Survey expectations are also tested for rational expectations in aggregate using the orthogonality test.     

On estimating the mean of the selected normal population under the LINEX loss function

Following Parsian and Farsipour (1999), we consider the problem of estimating the mean of the selected normal population, from two normal populations with unknown means and common known variance, under the LINEX loss function. Some admissibility results for a subclass of equivariant estimators are derived and a sufficient condition for the inadmissibility of an arbitrary equivariant estimator is provided. As a consequence, several of the estimators proposed by Parsian and Farsipour (1999) are shown to be inadmissible and better estimators are obtained. Received January 2001/Revised May 2002     

On the goodness-of-fit procedure for normality based on the empirical characteristic function for ranked set sampling data

The behaviour of the goodness-of-fit procedure for normality based on weighted integrals of the empirical characteristic function, discussed in the case of i.i.d. data, for instance, in Epps and Pulley (Biometrika 70:723–726, 1983), is considered here in the context of ranked set sampling (RSS) data. In the RSS context, we obtain the limiting distribution of the empirical characteristic process and perform a power study, against a broad set of alternatives, that enables an evaluation of the gain in power that occurs when a simple random sample is replaced by RSS data. The adaptation of the results obtained in the Gaussian RSS setting to the case of other important location-scale families is also discussed.     

Randomized response technique for two sensitive characteristics at the same time

In this paper we present a randomized response technique which can be used to estimate the proportion of individuals having two sensitive characteristics at the same time. The information obtained from this procedure can be used for weighting (post-stratification) purposes.     

Shrinkage estimation of the proportion in randomized response

This article considers the asymptotic estimation theory for the proportion in randomized response survey usinguncertain prior information (UPI) about the true proportion parameter which is assumed to be available on the basis of some sort of realistic conjecture. Three estimators, namely, the unrestricted estimator, the shrinkage restricted estimator and an estimator based on a preliminary test, are proposed. Their asymptotic mean squared errors are derived and compared. The relative dominance picture of the estimators is presented.     

An interactive decision support system for designing appropriate and adaptive sampling procedures in electric utility load research

Confidence interval estimation of customer demand for electricity plays a vital role in the capacity and financial planning of electric utility companies. Inaccurate or inadequate estimation could severely affect the economic efficiency of these companies. Selecting the appropriate sampling procedure is, in turn, critical to ensuring success in the accurate estimation of electrical demand. Because of the nature and diversity of demand for electricity, however, classical sampling procedures have to be extensively modified. This paper describes a decision support system (DSS) that aids electric utility companies in selecting and designing appropriate sampling plans. The DSS adapts sophisticated statistical techniques to address all aspects of the sampling procedure.     

Constructing optimal randomized response designs with consideration for the level of privacy protection

This paper considers the problem of procuring truthful responses to estimate the proportion of qualitative characteristics. In order to protect the respondent's privacy, various techniques of generating randomized response rather than direct response are available in the literature. But the theory concerning them is generally developed with no attention to the required level of privacy protection. Illustrating two randomization devices, we show how optimal randomized response designs may be achieved. The optimal designs of forced response procedure as well as BHARGAVA and SINGH [Statistica (2000) Vol. 6, pp 315–321] procedure are shown to be special cases. In addition, the equivalent designs of optimal WARNER [Journal of the American Statistical Association (1965) Vol. 60, pp. 63–69] procedure are considered as well. It is also shown that stratification with proportional allocation will be helpful for improving the estimation efficiency.     

On the efficiency comparison of certain randomized response strategies

Comparisons between different randomized response strategies have already been performed by several workers but all have concentrated solely on comparing the variances of the appropriate estimators. A very little attention has been paid by these workers to the degree of privacy protection offered to the interviewees. In the present paper, an attempt has been made in this direction and some important randomized response strategies have been compared with the Warner's model, taking into account the aspect of privacy protection. Received February 2000     

On optimal allocations for estimating the surface of a random field

In general, the construction of optimal designs is apparently a difficult task for the approximation of a random field indexed by more than one dimension. Besides the rate of convergence of the minimum achievable error hardly anything is known until now. However, if there is an immanent structure present in the random field, then, taking this structure into account, improved estimates can be obtained. For this situation we present adequate designs which show, at least, a nearly optimal performance. work supported by 313/ARC/VII/93/151 of the DAAD work supported by Ku719/2-1 of the DFG     

Minimax estimation for the bounded mean of a bivariate normal distribution

A bivariate normal distribution is considered whose mean lies in an equilateral triangle. We show by a convexity argument that the three point prior having mass 1/3 at each of the edges is least favourable if the length of a side of the equilateral triangle is less than or equal to . Thus the corresponding Bayes estimator is minimax in that case. Numerical studies are given as well.     

Monitoring the mean and the variance of a stationary process

We deal with the problem of how deviations in the mean or the variance of a time series can be detected. Several simultaneous control charts are introduced which are based on EWMA (exponentially weighted moving average) statistics for the mean and the empirical variance. The combined X − S² EWMA chart is extended to time series. Further simultaneous charts are considered. The comparision of these schemes shows that the residual attempt must be favored if a variance change is present.