1Pontificia Universidad Católica de Valparaiso, Instituto de Matemática, Valparaíso, Chile. Universidad de Valparaiso, Centro de Investigación y Modelamiento de Fenómenos Aleatorios-Valparaiso, Valparaiso, Chile. Professor. Email: rfierro@ucv.cl
2Universidade de São Paulo, Instituto de Matemática e Estatística, São Paulo, Brasil. Doctoral student. Email: alejandreandrea@gmail.com
We developed an asymptotically optimal hypothesis test concerning the homogeneity of a Poisson process over various subintervals. Under the null hypothesis, maximum likelihood estimators for the values of the intensity function on the subintervals are determined, and are used in the test for homogeneity.
Key words: Poisson process, hypothesis testing, local alternatives, asymptotic distribution, asymptotically optimal, likelihood ratio test.
Una prueba de hipótesis asintótica para verificar homogeneidad de un proceso de Poisson sobre ciertos subintervalos es desarrollada. Bajo la hipótesis nula, estimadores máximo verosímiles para los valores de la función intensidad sobre los subintervalos mencionados son determinados y usados en el test de homogeneidad.
Palabras clave: proceso de Poisson, prueba de hipótesis, alternativas locales, distribución asintótica, asintóticamente óptimo, prueba de razón de verosimilitud.
Texto completo disponible en PDF
References
]]>1. Arkin, B. L. & Leemis, L. M. (2000), 'Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process from overlapping realizations', Management Science 46(7), 989-998. [ Links ]
2. Fierro, R. (2008), 'Test of homogeneity for some population models based on counting processes', Communications in Statistics-Theory and Methods 37(1), 46-54. [ Links ]
3. Henderson, S. G. (2003), 'Estimation for nonhomogeneous Poisson processes from aggregated data', Operation Research Letters 31(5), 375-382. [ Links ]
4. Karr, A. F. (1991), Point Processes and their Statistical Inference, Marcel Dekker, New York. [ Links ]
5. Kuhl, M. E. & Wilson, J. R. (2000), 'Least square estimation of nonhomogeneous Poisson processes', Journal of Statistical Computation and Simulation 67, 75-108. [ Links ]
]]>6. Kuhl, M. E., Wilson, J. R. & Johnson, M. A. (1997), 'Estimating and simulating Poisson processes having trends or multiple periodicities', IIE Transactions 29(3), 201-211. [ Links ]
7. Leemis, L. M. (1991), 'Nonparametric estimation of the cumulative intensity function for a nonhomogeneous Poisson process', Management Science 37(7), 886-900. [ Links ]
8. Leemis, L. M. (2004), 'Nonparametric estimation and variate generation for a nonhomogeneous Poisson process from event count data', IIE Transactions 36, 1155-1160. [ Links ]
9. Lehmann, E. L. (1999), Elements of Large-Sample Theory, Springer-Verlag, New York. [ Links ]
10. Lewis, P. A. W. & Shedler, G. S. (1979), 'Simulation of nonhomogeneous Poisson process by thinning', Naval Research Logistics 26(3), 403-413. [ Links ]
]]>11. Neyman, J. (1949), Contribution to the theory of the \chi^2 test, 'First Berkeley Symposium on Mathematical Statistics and Probability', p. 239-273. [ Links ]
12. Roberts, S. W. (1966), 'A comparison of some control chart procedures', Technometrics 8, 411-430. [ Links ]
13. Serfling, R. J. (1980), Approximation Theorems of Mathematical Statistics, Wiley and Sons, New York. [ Links ]
14. Shiryaev, A. N. (1963), 'On optimum methods in quickest detection problems', Theory Probability and Its Applications 8, 22-46. [ Links ]
Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:
@ARTICLE{RCEv34n3a02, ]]>
AUTHOR = {Fierro, Raúl and Tapia, Alejandra},
TITLE = {{Testing Homogeneity for Poisson Processes}},
JOURNAL = {Revista Colombiana de Estadística},
YEAR = {2011},
volume = {34},
number = {3},
pages = {421-432}
}