# Multiscale study of memory type simple ratio estimators in two stage sampling under exponentially weighted moving averages

## TL;DR

This paper introduces new memory-type estimators for two-stage sampling that improve efficiency and accuracy compared to existing methods.

## Contribution

The novelty lies in proposing memory-type ratio and exponential estimators for two-stage sampling under EWMA.

## Key findings

- The proposed estimators showed improved efficiency with minimum mean square error.
- Simulation and empirical results confirmed the superiority of the new estimators over existing approaches.
- Performance was evaluated under various EWMA smoothing constants (λ=0.3,0.5,0.75,0.9).

## Abstract

Two-stage cluster sampling is often employed in survey sampling when complete population information is not available. In this setting, the Exponentially Weighted Moving Average (EWMA) statistic offers an efficient way to estimate the population mean by incorporating both past and current data. Motivated by this, we propose a class of memory-type ratio and exponential estimators for estimating the population mean under a two-stage cluster sampling framework. Theoretical expressions for the biases and mean square errors (MSE) of the proposed estimators are derived. To evaluate their performance, a comprehensive simulation study was carried out, supplemented by an empirical application. Several special cases of the proposed estimators were also considered and compared with existing two-stage estimators. The analysis was performed under different values of the EWMA smoothing constant (λ=0.3,0.5,0.75,0.9). Both simulation and empirical results consistently show that the proposed memory-type two-stage ratio estimators outperform existing approaches, providing improved efficiency with minimum MSE.