Nonparametric Regression Approach to Bayesian Estimation

Jiti Gao and Han Hong ()

No 25/14, Monash Econometrics and Business Statistics Working Papers from Monash University, Department of Econometrics and Business Statistics

Abstract: Estimation of unknown parameters and functions involved in complex nonlinear econometric models is a very important issue. Existing estimation methods include generalised method of moments (GMM) by Hansen (1982) and others, efficient method of moments (EMM) by Gallant and Tauchen (1997), Markov chain Monte Carlo (MCMC) method by Chernozhukov and Hong (2003), and nonparametric simulated maximum likelihood estimation (NSMLE) method by Creel and Kristensen (2011), and Kristensen and Shin (2012). Except the NSMLE method, other existing methods do not provide closed-form solutions. This paper proposes non- and semi-parametric based closed-form approximations to the estimation and computation of posterior means involved in complex nonlinear econometric models. We first consider the case where the samples can be independently drawn from both the likelihood function and the prior density. The samples and observations are then used to nonparametrically estimate posterior mean functions. The estimation method is also applied to estimate the posterior mean of the parameter-of-interest on a summary statistic. Both the asymptotic theory and the finite sample study show that the nonparametric estimate of this posterior mean is superior to existing estimates, including the conventional sample mean.

Keywords: then proposes some non- and semi-parametric dimension reductions methods to deal with the case where the dimensionality of either the regressors or the summary statistics is large. Meanwhile; the paper develops a nonparametric estimation method for the case where the samples are obtained from using a resampling algorithm. The asymptotic theory shows that in each case the rate of convergence of the nonparametric estimate based on the resamples is faster than that of the conventional nonparametric estimation method by an order of the number of the resamples. The proposed models and estimation methods are evaluated through using simulated and empirical examples. Both the simulated and empirical examples show that the proposed nonparametric estimation based on resamples outperforms existing estimation methods. (search for similar items in EconPapers)
JEL-codes: C12 C14 C22 (search for similar items in EconPapers)
Date: 2014
New Economics Papers: this item is included in nep-ecm and nep-ore
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