Nonparametric Bayesian inference for multidimensional compound Poisson processes

Modern Stochastics: Theory and Applications

卷:2

Frank van der Meulen¹  Peter Spreij²  Shota Gugushvili³ 

[1] Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands;

[2] Korteweg–de Vries Institute for Mathematics, University of Amsterdam, P.O. Box 94248, 1090 GE Amsterdam, The Netherlands;

[3] Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands;

关键词: Decompounding;    multidimensional compound Poisson process;    nonparametric Bayesian estimation;    posterior contraction rate;   

DOI  :  10.15559/15-VMSTA20

来源: DOAJ

【 摘 要 】

Given a sample from a discretely observed multidimensional compound Poisson process, we study the problem of nonparametric estimation of its jump size density $r_{0}$ and intensity $\lambda _{0}$. We take a nonparametric Bayesian approach to the problem and determine posterior contraction rates in this context, which, under some assumptions, we argue to be optimal posterior contraction rates. In particular, our results imply the existence of Bayesian point estimates that converge to the true parameter pair $(r_{0},\lambda _{0})$ at these rates. To the best of our knowledge, construction of nonparametric density estimators for inference in the class of discretely observed multidimensional Lévy processes, and the study of their rates of convergence is a new contribution to the literature.

【 授权许可】

Unknown