A calibrated synthetic estimator for small area estimation

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Statistics in Transition New Series

Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics, Statistics & Probability

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VOLUME 22 , ISSUE 3 (September 2021) > List of articles

A calibrated synthetic estimator for small area estimation

Matthew Joshua Iseh * / Ekaette Inyang Enang *

Keywords : auxiliary variable, calibration estimation, simulation, synthetic estimation

Citation Information : Statistics in Transition New Series. Volume 22, Issue 3, Pages 15-30, DOI: https://doi.org/10.21307/stattrans-2021-025

License : (CC BY-NC-ND 4.0)

Received Date : 21-July-2020 / Accepted: 12-January-2021 / Published Online: 05-September-2021

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ABSTRACT

Synthetic estimators are known to produce estimates of population mean in areas where no sampled data are available, but such estimates are usually highly biased with invalid confidence statements. This paper presents a calibrated synthetic estimator of the population mean which addresses these problematic issues. Two known special cases of this estimator were obtained in the form of combined ratio and combined regression synthetic estimators, using selected tuning parameters under stratified sampling. In result, their biases and variance estimators were derived. The empirical demonstration of the usage involving the proposed calibrated estimators shows that they provide better estimates of the population mean than the existing estimators discussed in this study. In particular, the estimators were examined through simulation under three distributional assumptions, namely the normal, gamma and exponential distributions. The results show that they provide estimates of the mean displaying less relative bias and greater efficiency. Moreover, they prove more consistent than the existing classical synthetic estimator. The further evaluation carried out using the coefficient of variation provides additional confirmation of the calibrated estimator’s advantage over the existing ones in relation to small area estimation.

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