On Statistical Analysis of Compound Point Process
AbstractThe contribution deals with a stochastic process cumulating random increments at random moments (the compound point process). First, its martingale - compensator decomposition is recalled. Then a multiplicative form of the model with the regression on covariates, simultaneously for the intensity of counting process and for the distribution of increments, is considered. Finally, a semi-parametric model is studied, the uniform consistency
of estimators and the asymptotic normality of the process of residuals are proved.
Andersen, P., Borgan, O., Gill, R., and Keiding, N. (1993). Models based on counting processes. New York: Springer.
Andersen, P., and Gill, R. (1982). Cox’s regression model for counting processes: A large sample study. Annals of Statist., 10, 1100-1120.
Brémaud, P. (1981). Point processes and queues: Martingale dynamics. Berlin: Springer.
Scheike, T. (1994). Parametric regression for longitudinal data with counting process measurement times. Scand. J. Statist., 21, 245-263.
Volf, P. (2000). On cumulative process model and its statistical analysis. Kybernetika, 36, 165-176.
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