Adaptive Bayesian Inference in Nonlinear Regression Models

44 Pages Posted: 15 Apr 2017

See all articles by Ji Yeon Yang

Ji Yeon Yang

Kumoh National Institute of Technology

Jungmo Yoon

Hanyang University

Date Written: June 16, 2016

Abstract

There has been continuing interest in Bayesian regressions without imposing any parametric assumption on the error distribution, but the asymptotic efficiency of such procedures has not been fully understood yet. In this article, we consider semiparametric Bayesian nonlinear regression models. We do not impose a parametric form for the likelihood function; rather, we treat the true density function of error terms as an infinite dimensional nuisance parameter and estimate it nonparametrically. Thereafter, we conduct conventional parametric Bayesian inference using MCMC methods. We derive the asymptotic properties of the resulting estimator and identify conditions of adaptive estimation, under which our two-step Bayes estimator enjoys the same asymptotic normality as if we knew the true density. We compare accuracy and coverage of the adaptive Bayesian estimator with the maximum likelihood estimator in empirical studies on simulated and real data. In particular, we observe that the Bayesian inference may be superior in numerical stability for small sample sizes.

Keywords: Adaptive Estimation, Asymptotic Efficiency, Bayesian Semiparametrics, MCMC, Non-Linear Regression Models

Suggested Citation

Yang, Ji Yeon and Yoon, Jungmo, Adaptive Bayesian Inference in Nonlinear Regression Models (June 16, 2016). Available at SSRN: https://ssrn.com/abstract=2952576 or http://dx.doi.org/10.2139/ssrn.2952576

Ji Yeon Yang

Kumoh National Institute of Technology ( email )

Gumi City, Gyeongbuk
Korea, Republic of (South Korea)

Jungmo Yoon (Contact Author)

Hanyang University ( email )

Seoul 133-791
Korea

HOME PAGE: http://https://sites.google.com/site/jungmoyoon2

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