Academic Journal
A note on discriminating Poisson processes from other point processes with stationary inter arrival times
| العنوان: | A note on discriminating Poisson processes from other point processes with stationary inter arrival times |
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| المؤلفون: | Morvai, Gusztáv, Weiss, Benjamin |
| بيانات النشر: | Institute of Information Theory and Automation AS CR |
| سنة النشر: | 2019 |
| المجموعة: | DML-CZ (Czech Digital Mathematics Library) |
| مصطلحات موضوعية: | keyword:Point processes, msc:60G55 |
| الوصف: | summary:We give a universal discrimination procedure for determining if a sample point drawn from an ergodic and stationary simple point process on the line with finite intensity comes from a homogeneous Poisson process with an unknown parameter. Presented with the sample on the interval $[0,t]$ the discrimination procedure $g_t$, which is a function of the finite subsets of $[0,t]$, will almost surely eventually stabilize on either POISSON or NOTPOISSON with the first alternative occurring if and only if the process is indeed homogeneous Poisson. The procedure is based on a universal discrimination procedure for the independence of a discrete time series based on the observation of a sequence of outputs of this time series. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| تدمد: | 0023-5954 1805-949X |
| Relation: | mr:MR4055577; zbl:Zbl 07177917; reference:[1] Daley, D. J., Vere-Jones, D.: An introduction to the theory of point processes. Vol. II. General theory and structure. Second edition.In: Probability and its Applications. Springer, New York 2008. MR 2371524, 10.1007/978-0-387-49835-5; reference:[2] Haywood, J., Khmaladze, E.: On distribution-free goodness-of-fit testing of exponentiality.J. Econometr. 143 (2008), 5-18. MR 2384430, 10.1016/j.jeconom.2007.08.005; reference:[3] Kallenberg, O.: Foundations of modern probability. Second edition.In: Probability and its Applications. Springer-Verlag, New York 2002. MR 1876169, 10.1007/978-1-4757-4015-8; reference:[4] Lewis, P. A. W.: Some results on tests for Poisson processes.Biometrika 52 (1965), 1 and 2, 67-77. MR 0207107, 10.1093/biomet/52.1-2.67; reference:[5] Massart, P.: The tight constant in the Dvoretzky-Kiefer-Wolfowitz inequality.Ann. Probab. 18 (1990), 3, 1269-1283. Zbl 0713.62021, MR 1062069, 10.1214/aop/1176990746; reference:[6] Morvai, G., Weiss, B.: Testing stationary processes for independence.Ann. Inst. H. Poincare' Probab. Statist. 47 (2011), 4, 1219-1225. MR 2884232, 10.1214/11-aihp426; reference:[7] Ryabko, B., Astola, J.: Universal codes as a basis for time series testing.Statist. Methodol. 3 (2006), 375-397. MR 2252392, 10.1016/j.stamet.2005.10.004; reference:[8] Thorisson, H.: Coupling, stationarity, and regeneration.In: Probability and its Applications. Springer-Verlag, New York 2000. MR 1741181, 10.1007/978-1-4612-1236-2 |
| الاتاحة: | http://hdl.handle.net/10338.dmlcz/147952 |
| Rights: | access:Unrestricted ; rights:DML-CZ Czech Digital Mathematics Library, http://dml.cz/ ; rights:Institute of Mathematics AS CR, http://www.math.cas.cz/ ; conditionOfUse:http://dml.cz/use |
| رقم الانضمام: | edsbas.D6EC7C8F |
| قاعدة البيانات: | BASE |
Full Text Finder | تدمد: | 00235954 1805949X |
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