Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures

46 Pages Posted: 27 Oct 2007

See all articles by Mattias Villani

Mattias Villani

Sveriges Riksbank - Research Division; Stockholm University - Department of Statistics

Robert Kohn

University of New South Wales - School of Economics and School of Banking and Finance

Paolo Giordani

Norwegian Business School

Date Written: September 2007

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 components 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 mechanism 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

Suggested Citation

Villani, Mattias and Kohn, Robert and Giordani, Paolo, Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures (September 2007). Riksbank Research Paper Series No. 211, Available at SSRN: https://ssrn.com/abstract=1024701 or http://dx.doi.org/10.2139/ssrn.1024701

Mattias Villani (Contact Author)

Sveriges Riksbank - Research Division ( email )

S-103 37 Stockholm
Sweden

HOME PAGE: http://www.riksbank.com/research/villani

Stockholm University - Department of Statistics ( email )

Universitetsvägen 10
Stockholm, Stockholm SE-106 91
Sweden

HOME PAGE: http://www.riksbank.com/research/villani

Robert Kohn

University of New South Wales - School of Economics and School of Banking and Finance ( email )

Australian School of Business
Sydney NSW 2052, ACT 2600
Australia
+61 2 9385 2150 (Phone)

Paolo Giordani

Norwegian Business School ( email )

Nydalsveien 37
Oslo, 0442
Norway

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