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Regression density estimation using smooth adaptive Gaussian mixtures

[journal article]

Villani, Mattias; Kohn, Robert; Giordani, Paolo

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Abstract We model a regression density flexibly 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 fewer 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 flexible high-dimensional 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, but also that special cases of the general model are interesting models for economic data.
Classification Methods and Techniques of Data Collection and Data Analysis, Statistical Methods, Computer Methods; Economic Statistics, Econometrics, Business Informatics
Free Keywords Bayesian inference; Markov Chain Monte Carlo; Mixture of experts; Nonparametric estimation; Splines; Value-at-Risk; Variable selection;
Document language English
Publication Year 2009
Page/Pages p. 155-173
Journal Journal of Econometrics, 153 (2009) 2
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)