The Novel HEWMA Exponential Type Mean Estimator under Ranked Set Sampling

Koçyiğit E. G.

Bilge International Journal of Science and Technology Research, cilt.9, sa.2, ss.53-63, 2025 (Hakemli Dergi)

Özet

Introduction
This study introduces a novel HEWMA-based memory-type exponential estimator for Ranked Set Sampling (RSS). The proposed estimator combines HEWMA control chart statistics with the exponential ratio estimator to enhance efficiency. By incorporating control chart statistics, memory-type estimators improve estimation accuracy by using both the current sample's mean and past mean(s), if available. This method is particularly beneficial for time-dependent repeated survey data or data collected from the same population at different time points.
Material and Methods
The proposed estimator's performance is evaluated through simulation studies using synthetic datasets, which simulate various scenarios with different correlation coefficients. An empirical study is also conducted using real-world data with a distinct structure. The evaluation focuses on the estimator's efficiency, considering factors such as sample size, correlation, and the number of past means incorporated.
Results
The simulation results demonstrate that incorporating at least one past sample mean value significantly enhances efficiency. Moreover, the estimator's effectiveness improves as both the correlation between samples and the number of old means (T) increase. The weight parameters of the HEWMA estimator play a critical role in determining its performance, with optimal results observed at low to medium correlation levels. The estimator consistently outperforms the existing alternatives in the real data analysis.
Discussion
The proposed HEWMA-based memory-type exponential estimator offers a more efficient alternative to the EWMA-type ratio estimator in the RSS method. The findings highlight the importance of selecting appropriate HEWMA weight parameters based on sample size and correlation. This approach substantially improves estimation accuracy, especially in time-dependent and longitudinal data scenarios. The proposed estimator performs particularly well under low to medium correlation conditions, and its applicability to real-world data further supports its practical utility.