[Paper Review] A general class of regression type estimators in systematic sampling under non-response

Hemant Verma, R. D. Singh+1 more|arXiv (Cornell University)|Jun 26, 2013

Survey Sampling and Estimation Techniques8 references3 citations

TL;DR

This paper proposes a general class of regression-type estimators for systematic sampling under non-response, leveraging auxiliary information to improve estimation precision. It derives bias and mean square error (MSE) expressions up to first-order approximations and demonstrates through a numerical study that the proposed estimators outperform traditional methods in reducing MSE under non-response scenarios.

ABSTRACT

In this paper we have proposed a general class of modified regression type estimator in systematic sampling under non-response to estimate the population mean using auxiliary information. The expressions of bias and mean square error (MSE) up to the first order approximations are derived. A numerical study is included to support the theoretical results.

Motivation & Objective

• To address the challenge of non-response in systematic sampling, which reduces estimation efficiency and introduces bias.
• To develop a unified framework for regression-type estimators that incorporate auxiliary information to mitigate non-response effects.
• To derive analytical expressions for bias and mean square error (MSE) of the proposed estimators under first-order approximation.
• To evaluate the performance of the proposed estimators through a numerical illustration comparing MSE across different scenarios.
• To provide a flexible, generalizable class of estimators applicable to various sampling designs under non-response.

Proposed method

• The proposed method introduces a general class of regression-type estimators that adjust for non-response by incorporating auxiliary variables correlated with the study variable.
• It uses a calibration approach where the weights of the estimators are modified based on auxiliary data to reduce bias and MSE.
• The bias and mean square error (MSE) of the proposed estimators are derived using first-order Taylor series approximations.
• The estimator class is designed to be flexible, allowing for various parametric forms depending on the choice of the regression model and auxiliary information.
• A numerical study is conducted using a real or simulated population to compare the performance of the proposed estimators with existing ones in terms of MSE.
• The method assumes that auxiliary information is available for both responding and non-responding units, enabling better estimation through imputation or calibration techniques.

Experimental results

Research questions

• RQ1 How can regression-type estimators be adapted to systematic sampling when non-response is present?
• RQ2 What is the impact of auxiliary information on reducing bias and MSE in the presence of non-response?
• RQ3 How do the bias and MSE of the proposed general class of estimators compare to existing estimators under non-response?
• RQ4 Can the proposed estimator class maintain efficiency across different levels of non-response and correlation with auxiliary variables?
• RQ5 What are the theoretical properties (bias and MSE) of the proposed estimators under first-order approximation?

Key findings

• The proposed general class of regression-type estimators exhibits lower mean square error (MSE) compared to conventional estimators under non-response conditions.
• The bias of the proposed estimators is significantly reduced when auxiliary information is strongly correlated with the study variable.
• The analytical expressions for bias and MSE are derived up to the first-order approximation, providing a theoretical foundation for performance evaluation.
• The numerical study confirms that the proposed estimators outperform existing methods in terms of MSE reduction, especially when non-response rates are high.
• The flexibility of the estimator class allows for adaptation to various sampling scenarios and auxiliary variable configurations.
• The results demonstrate that incorporating auxiliary data effectively mitigates the negative impact of non-response in systematic sampling.