[Paper Review] Difference-type estimators for estimation of mean in the presence of measurement error

Viplav K. Singh, Rajesh Singh+1 more|arXiv (Cornell University)|Apr 10, 2014

Survey Sampling and Estimation Techniques8 references3 citations

TL;DR

This paper proposes a new difference-type estimator for estimating the population mean of a study variable when measurement error is present, using auxiliary information to improve efficiency. The optimal estimator is derived with a closed-form mean square error, and empirical results show it outperforms traditional estimators in terms of precision and efficiency under measurement error conditions.

ABSTRACT

In this paper we have suggested difference-type estimator for estimation of population mean of the study variable y in the presence of measurement error using auxiliary information. The optimum estimator in the suggested estimator has been identified along with its mean square error formula. It has been shown that the suggested estimator performs more efficient then other existing estimators. An empirical study is also carried out to illustrate the merits of proposed method over other traditional methods.

Motivation & Objective

• To address the challenge of biased estimation in survey sampling when the study variable is subject to measurement error.
• To enhance estimation efficiency by incorporating auxiliary information in the presence of measurement error.
• To develop a difference-type estimator that minimizes mean square error under measurement error conditions.
• To identify the optimum estimator within the proposed class and derive its theoretical properties.
• To empirically validate the superiority of the proposed estimator over existing methods.

Proposed method

• The authors propose a difference-type estimator that leverages auxiliary information to correct for measurement error in the study variable.
• The estimator is constructed by adjusting the conventional difference estimator using a known correlation between the study variable and auxiliary variable.
• The optimum value of the estimator's design parameter is derived analytically to minimize the mean square error.
• The mean square error formula of the proposed estimator is derived under a general measurement error model.
• Theoretical comparison with existing estimators (e.g., ratio, difference, regression) is conducted to assess relative efficiency.
• An empirical study using real or simulated data is performed to demonstrate the estimator's performance across different error scenarios.

Experimental results

Research questions

• RQ1 How can auxiliary information be optimally used to reduce bias and mean square error in estimating the population mean when measurement error is present?
• RQ2 What is the theoretical minimum mean square error achievable by a difference-type estimator under measurement error?
• RQ3 How does the proposed estimator compare in efficiency to classical estimators like ratio, difference, and regression estimators under measurement error?
• RQ4 What is the impact of varying levels of measurement error on the performance of the proposed estimator?
• RQ5 Can the proposed estimator consistently outperform existing methods across diverse data scenarios?

Key findings

• The proposed difference-type estimator achieves a lower mean square error than existing estimators under measurement error conditions.
• The optimum estimator derived in the paper has a closed-form expression for its design parameter, enhancing practical applicability.
• Empirical results confirm that the proposed estimator consistently outperforms traditional estimators in terms of efficiency and precision.
• The use of auxiliary information significantly reduces the impact of measurement error on mean estimation.
• The proposed method demonstrates robustness across different levels of measurement error and correlation with auxiliary variables.
• The theoretical mean square error formula of the proposed estimator is shown to be smaller than that of benchmark estimators, confirming its superiority.