On Statistical Analysis of Compound Point Process
DOI:
https://doi.org/10.17713/ajs.v35i2&3.387Abstract
The 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 consistencyof estimators and the asymptotic normality of the process of residuals are proved.
References
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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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