Copula Based Factorization in Bayesian Multivariate Infinite Mixture Models
Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. In economics, they have been particularly useful in estimating nonparametric distributions of latent variables. However, these models have been rarely applied in more than one dimension. Indeed, the multivariate case suffers from the curse of dimensionality, with a rapidly increasing number of parameters needed to jointly characterize each mixing component. In this paper, we propose a factorization scheme for nonparametric mixture models whereby each marginal dimension in the mixing parameter space is modeled separately, linked by a nonparametric random copula function. Specifically, we consider nonparametric univariate Gaussian mixtures for the marginals and a multivariate random Bernstein polynomial copula for the link function, under Dirichlet process priors. We show that this scheme leads to an improvement in the precision of a density estimate in finite samples, providing a suitable tool for applications in higher dimensions. We derive weak posterior consistency of the copula-based mixing scheme for general kernel types under high-level conditions, and strong posterior consistency for the specific Bernstein-Gaussian mixture model.
(This abstract was borrowed from another version of this item.)
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- Burda, Martin & Harding, Matthew & Hausman, Jerry, 2008.
"A Bayesian mixed logit-probit model for multinomial choice,"
Journal of Econometrics,
Elsevier, vol. 147(2), pages 232-246, December.
- Martin Burda & Matthew Harding & Jerry Hausman, 2008. "A Bayesian mixed logit-probit model for multinomial choice," CeMMAP working papers CWP23/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Mark J. Jensen & John M. Maheu, 2009.
"Bayesian Semiparametric Stochastic Volatility Modeling,"
Working Paper Series
23_09, The Rimini Centre for Economic Analysis.
- Jensen, Mark J. & Maheu, John M., 2010. "Bayesian semiparametric stochastic volatility modeling," Journal of Econometrics, Elsevier, vol. 157(2), pages 306-316, August.
- Mark J Jensen & John M Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," Working Papers tecipa-314, University of Toronto, Department of Economics.
- Mark J. Jensen & John M. Maheu, 2008. "Bayesian semiparametric stochastic volatility modeling," FRB Atlanta Working Paper 2008-15, Federal Reserve Bank of Atlanta.
- Chib, Siddhartha & Hamilton, Barton H., 2002. "Semiparametric Bayes analysis of longitudinal data treatment models," Journal of Econometrics, Elsevier, vol. 110(1), pages 67-89, September.
- Zheng, Yanbing, 2011. "Shape restriction of the multi-dimensional Bernstein prior for density functions," Statistics & Probability Letters, Elsevier, vol. 81(6), pages 647-651, June.
- Yanbing Zheng & Jun Zhu & Anindya Roy, 2010. "Nonparametric Bayesian inference for the spectral density function of a random field," Biometrika, Biometrika Trust, vol. 97(1), pages 238-245.
- Chen, Xiaohong & Fan, Yanqin & Tsyrennikov, Viktor, 2006.
"Efficient Estimation of Semiparametric Multivariate Copula Models,"
Journal of the American Statistical Association,
American Statistical Association, vol. 101, pages 1228-1240, September.
- Xiaohong Chen & Yanqin Fan & Victor Tsyrennifov, 2004. "Efficient Estimation of Semiparametric Multivariate Copula Models," Vanderbilt University Department of Economics Working Papers 0420, Vanderbilt University Department of Economics.
- A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
- Sonia Petrone & Larry Wasserman, 2002. "Consistency of Bernstein polynomial posteriors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(1), pages 79-100.
- Conley, Timothy G. & Hansen, Christian B. & McCulloch, Robert E. & Rossi, Peter E., 2008. "A semi-parametric Bayesian approach to the instrumental variable problem," Journal of Econometrics, Elsevier, vol. 144(1), pages 276-305, May.
- Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(03), pages 535-562, June.
- Leisen, Fabrizio & Lijoi, Antonio, 2011. "Vectors of two-parameter Poisson-Dirichlet processes," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 482-495, March.
- Sonia Petrone, 1999. "Random Bernstein Polynomials," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(3), pages 373-393.
- Ausin, M. Concepcion & Lopes, Hedibert F., 2010. "Time-varying joint distribution through copulas," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2383-2399, November.
- Michael Pitt & David Chan & Robert Kohn, 2006. "Efficient Bayesian inference for Gaussian copula regression models," Biometrika, Biometrika Trust, vol. 93(3), pages 537-554, September.
- Keisuke Hirano, 2002. "Semiparametric Bayesian Inference in Autoregressive Panel Data Models," Econometrica, Econometric Society, vol. 70(2), pages 781-799, March.
- Paolo Giordani & Xiuyan Mun & Robert Kohn, 2012. "Efficient Estimation of Covariance Matrices using Posterior Mode Multiple Shrinkage," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 154-192, December.
- Axel Tenbusch, 1994. "Two-dimensional Bernstein polynomial density estimators," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 41(1), pages 233-253, December.
- RodrÃguez, Abel & Dunson, David B. & Gelfand, Alan E., 2010. "Latent Stick-Breaking Processes," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 647-659.
- Kim Jin Gyo & Menzefricke Ulrich & Feinberg Fred M., 2004. "Assessing Heterogeneity in Discrete Choice Models Using a Dirichlet Process Prior," Review of Marketing Science, De Gruyter, vol. 2(1), pages 1-41, January.
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