Application to Road Traffic Accidents: An Almost Unbiased Estimator for Population Mean Under Ranked Set Sampling and Stratified Ranked Set Sampling

Document Type

Article

Publication Title

Journal of Statistical Theory and Applications

Abstract

Ranked Set Sampling (RSS) serves as an effective and efficient alternative to Simple Random Sampling (SRS), especially when ranking items is easier than taking precise measurements. Stratified sampling is used for better estimation when the population is heterogeneous. In this work, we introduce a new family of nearly unbiased estimators for estimating the population mean under the RSS and SRSS framework. These estimators are formulated as linear combinations of three established estimators and are specifically developed to minimize bias to the first order. We analytically derive their theoretical properties, including bias and Mean Squared Error (MSE), to evaluate their statistical performance. To support our theoretical claims, we apply the proposed estimators to real-world data and perform extensive simulation experiments under varying sample sizes and correlation settings. We benchmark our estimator against existing ones such as the conventional sample mean, the exponential ratio estimator, and the logarithmic estimator. The assessment is based on key metrics like MSE and Percentage Relative Efficiency (PRE). The findings consistently show that the proposed estimator yields lower MSE and higher PRE, indicating better accuracy and efficiency under both sampling frames. Furthermore, its near-unbiased behaviour enhances its practical applicability, particularly in scenarios where ranking is more feasible than direct measurement.

DOI

10.1007/s44199-025-00145-8

Publication Date

1-1-2025

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