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Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures

Mattias Villani, Robert Kohn () and Paolo Giordani ()

No 211, Working Paper Series from Sveriges Riksbank (Central Bank of Sweden)

Abstract: We model a regression density nonparametrically so that at each value of the covariates the density is a mixture of normals with the means, variances and mixture probabilities of the com- ponents changing smoothly as a function of the covariates. The model extends existing models in two important ways. First, the components are allowed to be heteroscedastic regressions as the standard model with homoscedastic regressions can give a poor fit to heteroscedastic data, especially when the number of covariates is large. Furthermore, we typically need a lot fewer heteroscedastic components, which makes it easier to interpret the model and speeds up the computation. The second main extension is to introduce a novel variable selection prior into all the components of the model. The variable selection prior acts as a self-adjusting mech- anism that prevents overfitting and makes it feasible to fit high-dimensional nonparametric surfaces. We use Bayesian inference and Markov Chain Monte Carlo methods to estimate the model. Simulated and real examples are used to show that the full generality of our model is required to fit a large class of densities.

Keywords: Bayesian inference; Markov Chain Monte Carlo; Mixture of Experts; Predictive inference; Splines; Value-at-Risk; Variable selection (search for similar items in EconPapers)
JEL-codes: E50 (search for similar items in EconPapers)
Pages: 46 pages
Date: 2007-09-01
New Economics Papers: this item is included in nep-ecm, nep-for and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2) Track citations by RSS feed

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