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Nonparametric Bayesian inference for multidimensional compound Poisson processes. (English) Zbl 1349.62115
Summary: 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.

MSC:
62G07 Density estimation
60G51 Processes with independent increments; Lévy processes
62F15 Bayesian inference
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
62M30 Inference from spatial processes
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