On Bernstein type inequalities for stochastic integrals of multivariate point processes

Hanchao Wang, Zhengyan Lin and Zhonggen Su

Stochastic Processes and their Applications, 2019, vol. 129, issue 5, 1605-1621

Abstract: In this paper, we first obtain a Bernstein type of concentration inequality for stochastic integrals of multivariate point processes under some conditions through the Doléans-Dade exponential formula, and then derive a uniform exponential inequality using a generic chaining argument. As a direct consequence, we obtain an upper bound for a sequence of discrete time martingales indexed by a class of functionals. Finally, we apply the uniform exponential bound to nonparametric maximum likelihood estimators and provide a rate of convergence in terms of Hellinger distance, which is an improvement of earlier work of van de Geer (1995).

Keywords: Bernstein inequality; Doléans-Dade exponential; Generic chaining method; Kakutani–Hellinger distance; Multivariate point process (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1016/j.spa.2018.05.014

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