期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2017
卷号：79
期号：2
页码：336-354
DOI：10.1007/s13171-017-0105-7
语种：English
出版社：Indian Statistical Institute
摘要：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 \(L_{\infty }\) -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.
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