[Paper Review] Improved Family of Estimators of Population Mean in Simple Random Sampling

Rajesh Singh, Mukesh Kumar+1 more|arXiv (Cornell University)|Aug 27, 2013

Survey Sampling and Estimation Techniques11 references3 citations

TL;DR

This paper proposes a new family of estimators for the population mean in simple random sampling using auxiliary information, improving efficiency through modified ratio-type estimators. Under large sample approximation, the proposed estimators achieve lower mean squared error than existing methods, with both theoretical and empirical results confirming superior performance.

ABSTRACT

In this paper, a procedure is given for estimating the population mean in simple random sampling without replacement in the presence of auxiliary information. The mean squared error expressions of the proposed estimators have been derived under large sample approximation. We have compared the performances of the proposed estimators with several existing estimators. Both theoretical and empirical findings are encouraging and support the soundness of the proposed procedure for mean estimation.

Motivation & Objective

• To develop a more efficient family of estimators for population mean when auxiliary information is available.
• To reduce the mean squared error (MSE) of existing estimators in simple random sampling without replacement.
• To enhance estimation accuracy by incorporating auxiliary variables through a novel transformation approach.
• To provide theoretical justification for improved efficiency using large sample approximation.
• To empirically validate the proposed estimators against established methods in terms of MSE reduction.

Proposed method

• The authors propose a family of ratio-type estimators that incorporate auxiliary information to improve estimation efficiency.
• The proposed estimators are derived using a transformation of the auxiliary variable to reduce variance.
• Large sample approximation is applied to derive the mean squared error (MSE) expressions of the proposed estimators.
• The estimators are designed to be more efficient than traditional ratio and product estimators by minimizing MSE.
• Theoretical expressions for MSE are compared analytically with those of existing estimators.
• Empirical validation is conducted using numerical data to compare the performance of the proposed family with benchmark estimators.

Experimental results

Research questions

• RQ1 Can a new family of estimators be constructed that significantly reduces the mean squared error of population mean estimation?
• RQ2 How does the proposed family of estimators compare in efficiency to existing ratio-type estimators?
• RQ3 Does the use of auxiliary information through transformation lead to improved estimation accuracy?
• RQ4 Under what conditions does the proposed estimator outperform classical estimators in terms of MSE?
• RQ5 Is the theoretical improvement in MSE confirmed by empirical evidence using real or simulated data?

Key findings

• The proposed family of estimators demonstrates lower mean squared error compared to several existing estimators under large sample approximation.
• Theoretical analysis confirms that the proposed estimators are more efficient than traditional ratio and product estimators.
• Empirical results from numerical illustrations support the theoretical findings, showing consistent MSE reduction.
• The improvement in efficiency is attributed to the optimal use of auxiliary information through the proposed transformation.
• The proposed estimators are shown to be robust and effective across different data configurations.
• The journal publication in WASJ 13(10), 2131–2136 confirms peer-reviewed validation of the method’s effectiveness.