ROBUST BAYESIAN HIERARCHICAL ESTIMATION OF THE FINITE POPULATION  MEAN UNDER UNEQUAL CLUSTER SAMPLING

Nkan Iso-Osene Doris; Adidaumbe Ugbe Thomas; Inyang Enang Ekaette; Elendu Onwukwe Christian; Ogum Uket Joy; Asu Owan Raphael

Nkan Iso-Osene Doris Department of Statistics, University of Calabar, Calabar, Nigeria
Adidaumbe Ugbe Thomas Department of Statistics, University of Calabar, Calabar, Nigeria
Inyang Enang Ekaette Department of Statistics, University of Calabar, Calabar, Nigeria
Elendu Onwukwe Christian Department of Statistics, University of Calabar, Calabar, Nigeri
Ogum Uket Joy Department of Statistics, University of Calabar, Calabar, Nigeria
Asu Owan Raphael Department of Statistics, University of Calabar, Calabar, Nigeria

Abstract

Cluster sampling is widely used for studying populations that are naturally grouped, but classical
estimators can perform poorly when observations contain outliers. In this study, we propose a robust
Bayesian hierarchical estimator for estimating the finite population mean under unequal cluster
sampling. We show that the proposed estimator has a bounded influence function and stable
asymptotic mean-squared error (MSE) under ε-contamination, and we evaluated the performance
of the proposed estimator using both simulated and real datasets. Simulation results show that the
proposed estimator retains efficiency under correct model specification while significantly
improving robustness in contaminated settings, reducing point-estimation MSE by up to 40% and
posterior predictive error by up to 50%. An application to ecological parasite-load data further
demonstrates improved predictive stability and moderated mean estimates relative to the Gaussian
hierarchical model.
Key words: Cluster sampling; Bayesian hierarchical models; contamination; outliers; Student-t
distribution