On Bernstein Type Inequalities for Stochastic Integrals of Multivariate Point Processes
| Autor: | Wang, Hanchao, Lin, Zhengyan, Su, Zhonggen |
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| Rok vydání: | 2017 |
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| Druh dokumentu: | Working Paper |
| Popis: | We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform exponential inequality using a generic chaining argument. As applications, we obtain a upper bound for a sequence of discrete time martingales indexed by a class of functionals, and so derive the rate of convergence for nonparametric maximum likelihood estimators, which is an improvement of earlier work of van de Geer. Comment: 18 pages |
| Databáze: | arXiv |
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