Median estimation in the presence of non-response using randomised response technique

Attique Hussain; Muhammad Shahid Mahmood; Amjad Mahmood; Ayesha Ashraf

doi:10.47264/idea.nasij/4.2.7

Authors

Attique Hussain National College of Business Administration and Economics, Lahore, Pakistan. https://orcid.org/0009-0004-2183-7739
Muhammad Shahid Mahmood National College of Business Administration and Economics, Lahore, Pakistan. https://orcid.org/0009-0003-6577-9991
Amjad Mahmood Punjab College of Information Technology, Lahore, Pakistan | Hailey College of Commerce, University of the Punjab, Lahore, Pakistan. https://orcid.org/0009-0006-6396-2305
Ayesha Ashraf Monash Business School, Monash University, Victoria, Australia.

DOI:

https://doi.org/10.47264/idea.nasij/4.2.7

Keywords:

RRT, Non-response, regression cum ratio, exponential expansions, optimum value, relative competence percentage, theory of parameter estimation

Abstract

The theory of parameter estimation was developed a long time ago and is currently a widely accepted scientific approach. In some situations where the mean has to deal with the effect of extreme values, the median can be used instead. As there is almost little literature available on median estimation in the existence of non-responsive with the help of the Randomized Response Technique (RRT), the main objective of this paper was to develop a basic theoretical framework for median estimation in the existence of non-responsive with the help of RRT. In this work, we suggested median estimation for delicate variables in auxiliary information using a randomised response model. We have suggested a basic median estimator, product, ratio, exponential product, exponential ratio, and regression cum ratio estimation of the median for non-response by utilising RRT. The mathematical derivations for optimum values of constants, biasness, and Mean Square Error (MSE) of purposed estimators result from the application of well-known Taylor and exponential expansions. The performance of mentioned estimators is evaluated through the numerical study of two populations which discovered the regression cum ratio estimate is more proficient than the remaining estimations mentioned in this article.

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