Modeling Conditional Densities Using Finite Smooth Mixtures

Riksbank Research Paper Series No. 76

Sveriges Riksbank Working Paper Series No. 245

22 Pages Posted: 27 Jan 2011

See all articles by Robert Kohn

Robert Kohn

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

Feng Li

Peking University - Guanghua School of Management

Mattias Villani

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

Date Written: August 2010

Abstract

Smooth mixtures, i.e. mixture models with covariate-dependent mixing weights, are very useful flexible models for conditional densities. Previous work shows that using too simple mixture components for modeling heteroscedastic and/or heavy tailed data can give a poor fit, even with a large number of components. This paper explores how well a smooth mixture of symmetric components can capture skewed data. Simulations and applications on real data show that including covariate-dependent skewness in the components can lead to substantially improved performance on skewed data, often using a much smaller number of components. Furthermore, variable selection is effective in removing unnecessary covariates in the skewness, which means that there is little loss in allowing for skewness in the components when the data are actually symmetric. We also introduce smooth mixtures of gamma and log-normal components to model positively-valued response variables.

Keywords: Bayesian inference, Markov chain Monte Carlo, Mixture of Experts, Variable selection

Suggested Citation

Kohn, Robert and Li, Feng and Villani, Mattias, Modeling Conditional Densities Using Finite Smooth Mixtures (August 2010). Riksbank Research Paper Series No. 76, Sveriges Riksbank Working Paper Series No. 245, Available at SSRN: https://ssrn.com/abstract=1711194 or http://dx.doi.org/10.2139/ssrn.1711194

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)

Feng Li

Peking University - Guanghua School of Management ( email )

Peking University
Beijing, Beijing 100871
China

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

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