Bayesian Nonparametric Models for Conditional Densities Based on Orthogonal Polynomials

Andriy Norets () and Marco Stenborg Petterson ()
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Andriy Norets: Brown University
Marco Stenborg Petterson: University of Naples Federico II and CSEF, https://csef.it/people/marco-stenborg-petterson/

CSEF Working Papers from Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy

Abstract: The paper considers a nonparametric Bayesian model for conditional densities. The model considered is a mixture of orthogonal polynomials with a prior on the number of components. The use of orthogonal polynomials allows for a great deal of flexibility in applications while maintaining useful approximation properties. We provide the posterior contraction rate in the case of Legendre polynomials. The algorithm proposed allows for cross-dimensional moves, allowing it to choose the optimal number of terms in the series expansion conditional on a penalty parameter. We also provide Monte Carlo simulations that show how well the model approximates known distributions also in finite sample situations.

Keywords: Bayesian nonparametrics; orthogonal polynomials; variable dimensions model (search for similar items in EconPapers)
JEL-codes: C11 C13 C14 (search for similar items in EconPapers)
Date: 2024-12-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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