Nonparametric Regression Density Estimation Using Smoothly Varying Normal Mixtures
AbstractWe 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.
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Bibliographic InfoPaper provided by Sveriges Riksbank (Central Bank of Sweden) in its series Working Paper Series with number 211.
Length: 46 pages
Date of creation: 01 Sep 2007
Date of revision:
Bayesian inference; Markov Chain Monte Carlo; Mixture of Experts; Predictive inference; Splines; Value-at-Risk; Variable selection;
Find related papers by JEL classification:
- E50 - Macroeconomics and Monetary Economics - - Monetary Policy, Central Banking, and the Supply of Money and Credit - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-11-24 (All new papers)
- NEP-ECM-2007-11-24 (Econometrics)
- NEP-FOR-2007-11-24 (Forecasting)
- NEP-MAC-2007-11-24 (Macroeconomics)
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