Bal Kishan Dass

A Three-Stage Optional Randomized Response Model

In Gupta et al. (2010; 2011), it was observed that introduction of a truth element in an optional randomized response model can improve the efficiency of the mean estimator. However, a large value of the truth parameter (T) may be needed if the underlying question is highly sensitive. This can jeopardize respondent cooperation. In what we call a “three-stage optional randomized response model,” a known proportion (T) of the respondents is asked to tell the truth, another known proportion (F) of the respondents is asked to provide a scrambled response, and the remaining respondents are instructed to provide a response following the usual optional randomized response strategy where a respondent provides a truthful response (or a scrambled response) depending on whether he/she considers the question nonsensitive (or sensitive). This is done anonymously based on color-coded cards that the researcher cannot see. In this article we show that a three-stage model may turn out to be more efficient than the corresponding two-stage model, and with a smaller value of T. Greater respondent cooperation will be an added advantage of the three-stage model.

Generalized Scrambling in Quantitative Optional Randomized Response Models

Huang (2010) proposed an optional randomized response model using a linear combination scrambling which is a generalization of the multiplicative scrambling of Eichhorn and Hayre (1983) and the additive scrambling of Gupta et al. (2006, 2010). In this article, we discuss two main issues. (1) Can the Huang (2010) model be improved further by using a two-stage approach?; (2) Does the linear combination scrambling provide any benefit over the additive scrambling of Gupta et al. (2010)? We will note that the answer to the first question is “yes” but the answer to the second question is “no.”

Extended Varshamov- Gilbert and sphere-packing bounds for burst-correcting codes (Corresp.)

The study of burst-error-correcting codes has generally been made without weight considerations while the random-error-correcting capabilities of a linear code largely depend upon the minimum weight. In this correspondence we have obtained extensions of the Varshamov-Gilbert and sphere-packing hounds to burst-error-correcting codes.

On 2-Repeated Burst Error Detecting Codes

There are several kinds of burst errors for which error detecting and correcting codes have been constructed. In this paper, we introduce a new kind of burst error which will be termed as ‘repeated burst error’. Linear codes capable of detecting such errors have been studied. Further, codes capable of detecting and simultaneously correcting such errors have also been dealt with. The paper obtains lower and upper bounds on the number of parity-check digits required for such codes. An example of such a code has also been provided.

On a Burst-Error Correcting Code

This paper presents lower and upper bounds on the number of parity-check digits required for a linear code that corrects errors which are bursts of length b (fixed) of a specified type.

A Sufficient Bound for Codes Correcting Bursts with Weight Constraint

An upper bound on the sufficient number of panty-cheek positions of a hnear code capable of correcting bursts of a given length or less having a weight constraint over them is p r e s e n t e d An example of a code which corrects all bursts of length 3 or less that have weight 2 or less is given.

Ratio Estimation of Finite Population Mean Using Optional Randomized Response Models

Auxiliary information is commonly used in sample surveys in order to achieve higher precision in the estimates. In this article we are concerned with the utilization of auxiliary information in the estimation stage in simple random sampling without replacement (SRSWOR), making use of an optional randomized response model proposed by Gupta et al. (2010). The underlying assumption is that the primary variable is sensitive in nature but a nonsensitive auxiliary variable exists that is positively correlated with the primary variable. We propose a ratio estimator of finite population mean and call it the additive ratio estimator. Expressions for the bias and mean square error of the proposed estimator are obtained to first order of approximation. Efficiency comparisons with the ordinary optional randomized response technique (RRT) mean estimator of Gupta et al. (2010) are carried out both theoretically and numerically. A simulation study is presented to evaluate the performance of the proposed estimator.

Estimation of Finite Population Mean Using Optional RRT Models in the Presence of Nonsensitive Auxiliary Information

SYNOPTIC ABSTRACT Sousa, Shabbir, Corte-Real, and Gupta (2010) and Gupta, Shabbir, Sousa, and Corte-Real (2012) have presented ratio and regression estimators for the finite population mean of a sensitive study variable utilizing nonsensitive auxiliary information. We improve the results further by using optional scrambling. In the process, we also estimate the sensitivity level of the underlying sensitive question. We compare the proposed method with Sousa et al. (2010) and Gupta et al. (2012) estimators.

Some Combinatorial Aspects of m-Repeated Burst Error Detecting Codes

There are several kinds of burst errors for which error detecting and error correcting codes have been constructed. In this paper, we consider a new kind of burst error which will be termed as ‘m-repeated burst error of length b(fixed)’. The paper presents lower bounds on the number of parity-check digits required for a linear code that is capable of detecting errors which are m-repeated burst errors of length b(fixed). Further, codes capable of detecting and simultaneously correcting such errors have also been studied.

Burst Error Locating Linear Codes

This paper presents a lower and an upper bound on the number of parity-check digits required for a linear code that locates a single sub-block containing errors which are in the form of bursts.