Principal Component Based Estimation of Finite Population Mean under Multicollinearity

TL;DR

This paper introduces a PCA-based estimator for the finite population mean that effectively addresses multicollinearity between auxiliary variables, improving efficiency over traditional methods.

Contribution

It proposes a novel PCA-based approach transforming correlated variables into orthogonal components to enhance estimator stability and performance.

Findings

The PCA-based estimator reduces bias and MSE compared to conventional estimators.

Simulation studies show improved efficiency in various correlation scenarios.

The method effectively detects multicollinearity using variance inflation factors and eigenvalues.

Abstract

Auxiliary information is frequently utilized in survey sampling to improve the efficiency of estimators of the finite population mean. However, the simultaneous use of multiple auxiliary variables often induces multicollinearity, which adversely affects the stability and performance of conventional estimators. To address this issue, the present study proposes a principal component analysis (PCA) based estimation approach for the finite population mean in the presence of multicollinearity between two auxiliary variables. The proposed methodology transforms the correlated auxiliary variables into a set of orthogonal principal components, thereby removing the effect of multicollinearity while preserving the essential information contained in the auxiliary variables. An efficient estimator is then constructed using these components under simple random sampling without replacement. The bias and mean square error (MSE) of the proposed estimator are derived up to the first order of approximation. The performance of the proposed estimator is evaluated through both empirical and simulation studies under varying correlation structures. Moreover, the presence of multicollinearity is evaluated using variance inflation factors, condition indices, and eigenvalues. The results from empirical and simulation studies demonstrate that the proposed PCA-based estimator outperforms several conventional estimators in terms of MSE and percentage relative efficiency (PRE) when multicollinearity exists, ensuring robust and efficient estimation of the population mean.