[Paper Review] Ratio Estimators in Simple Random Sampling when Study Variable is an Attribute

Rajesh Singh, Mukesh Kumar+1 more|arXiv (Cornell University)|Nov 3, 2010

Survey Sampling and Estimation Techniques5 citations

TL;DR

This paper proposes a family of ratio estimators for estimating the population mean when the study variable is qualitative (an attribute) in simple random sampling. By leveraging auxiliary information on a related attribute, the authors derive bias and mean square error expressions, demonstrating through an empirical study that their proposed estimators outperform traditional methods in terms of efficiency and accuracy.

ABSTRACT

In this paper we have suggested a family of estimators for the population mean when study variable itself is qualitative in nature. Expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An empirical study has been carried out to show the superiority of the constructed estimator over others.

Motivation & Objective

• To develop improved ratio estimators for population mean estimation when the study variable is qualitative (an attribute), not quantitative.
• To incorporate auxiliary information from a related attribute variable to enhance estimation precision in simple random sampling.
• To derive analytical expressions for bias and mean square error (MSE) of the proposed family of estimators.
• To evaluate the performance of the proposed estimators empirically and compare them with existing methods.
• To establish conditions under which the proposed estimators achieve lower MSE than conventional ratio estimators.

Proposed method

• Proposes a family of ratio estimators using a transformation of the auxiliary attribute variable and the study variable in simple random sampling.
• Derives the first-order approximation of bias and mean square error (MSE) for the proposed estimators using Taylor series expansion.
• Utilizes the property that the study variable is binary (attribute) to define the estimator structure based on proportions or frequencies.
• Applies standard sampling theory to express the variance and MSE of the proposed estimators in terms of population parameters.
• Employs an empirical study using real or simulated data to compare the MSE of the proposed estimator with existing ratio estimators.
• Selects the optimal estimator from the family by minimizing the MSE expression under given constraints.

Experimental results

Research questions

• RQ1 Can a family of ratio estimators be effectively constructed when the study variable is qualitative (an attribute) rather than quantitative?
• RQ2 How does the bias and mean square error (MSE) of the proposed estimators compare to those of classical ratio estimators in attribute-based sampling?
• RQ3 Under what conditions does the proposed family of estimators achieve lower MSE than existing estimators?
• RQ4 How does the use of auxiliary attribute information improve estimation efficiency in simple random sampling?
• RQ5 What is the empirical performance of the proposed estimator relative to benchmark estimators in real or simulated data settings?

Key findings

• The proposed family of ratio estimators exhibits lower mean square error (MSE) compared to traditional ratio estimators when the study variable is an attribute.
• The bias of the proposed estimators is negligible under appropriate conditions, indicating high precision.
• Empirical results confirm that the proposed estimator outperforms existing estimators in terms of efficiency and accuracy.
• The optimal member of the proposed family achieves the minimum MSE among all considered estimators in the empirical study.
• Theoretical expressions for bias and MSE are valid and provide a reliable basis for selecting the best-performing estimator.
• The use of auxiliary attribute information significantly enhances estimation efficiency, especially when the correlation between the study and auxiliary variables is high.