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Volume 13
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Article

Small Area Estimation under Poisson–Dirichlet Process Mixture Models

by
Xiang Qiu
1,
Qinchun Ke
1,
Xueqin Zhou
1,* and
Yulu Liu
1,2
1
School of Science, Shanghai Institude of Technology, Shanghai 201418, China
2
Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, China
*
Author to whom correspondence should be addressed.
Axioms 2024, 13(7), 432; https://doi.org/10.3390/axioms13070432
Submission received: 18 April 2024 / Revised: 15 June 2024 / Accepted: 25 June 2024 / Published: 27 June 2024
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Abstract

In this paper, we propose an improved Nested Error Regression model in which the random effects for each area are given a prior distribution using the Poisson–Dirichlet Process. Based on this model, we mainly investigate the construction of the parameter estimation using the Empirical Bayesian(EB) estimation method, and we adopt various methods such as the Maximum Likelihood Estimation(MLE) method and the Markov chain Monte Carlo algorithm to solve the model parameter estimation jointly. The viability of the model is verified using numerical simulation, and the proposed model is applied to an actual small area estimation problem. Compared to the conventional normal random effects linear model, the proposed model is more accurate for the estimation of complex real-world application data, which makes it suitable for a broader range of application contexts.
Keywords: small area estimation; nested error regression models; Bayesian nonparametric estimation; Poisson–Dirichlet process; MCMC algorithm small area estimation; nested error regression models; Bayesian nonparametric estimation; Poisson–Dirichlet process; MCMC algorithm

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MDPI and ACS Style

Qiu, X.; Ke, Q.; Zhou, X.; Liu, Y. Small Area Estimation under Poisson–Dirichlet Process Mixture Models. Axioms 2024, 13, 432. https://doi.org/10.3390/axioms13070432

AMA Style

Qiu X, Ke Q, Zhou X, Liu Y. Small Area Estimation under Poisson–Dirichlet Process Mixture Models. Axioms. 2024; 13(7):432. https://doi.org/10.3390/axioms13070432

Chicago/Turabian Style

Qiu, Xiang, Qinchun Ke, Xueqin Zhou, and Yulu Liu. 2024. "Small Area Estimation under Poisson–Dirichlet Process Mixture Models" Axioms 13, no. 7: 432. https://doi.org/10.3390/axioms13070432

APA Style

Qiu, X., Ke, Q., Zhou, X., & Liu, Y. (2024). Small Area Estimation under Poisson–Dirichlet Process Mixture Models. Axioms, 13(7), 432. https://doi.org/10.3390/axioms13070432

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