Posterior Contraction Rates of Density Derivative Estimation

Weining Shen () and Subhashis Ghosal ()
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Weining Shen: University of California
Subhashis Ghosal: North Carolina State University

Sankhya A: The Indian Journal of Statistics, 2017, vol. 79, issue 2, No 8, 336-354

Abstract: Abstract In this paper, we study the problem of Bayesian estimation of derivatives of a density function on the unit interval. We use a finite random series prior based on B-splines and study the asymptotic properties of the posterior distribution under the setting of fixed smoothness of the true function. We obtain the posterior contraction rate under both the L 2- and L ∞ $L_{\infty }$ -distances. The rate under L 2-distance agrees with the minimax optimal rate. This result is then extended to the estimation of a multivariate density function on the unit cube and its mixed partial derivatives using tensor product B-splines.

Keywords: B-spline; Density derivative estimation; Nonparametric Bayes; Posterior contraction rate; Tensor product; Primary: 62G20; Secondary: 62G05 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s13171-017-0105-7

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