Smoothed estimator of the periodic hazard function

• Autorzy: Dudek A.
• Języki publikacji: EN

Abstrakty

EN

A smoothed estimator of the periodic hazard function is considered and its asymptotic probability distribution and bootstrap simultaneous confidence intervals are derived. Moreover, consistency of the bootstrap method is proved and some applications of the developed theory are presented. The bootstrap method is based on the phase-consistent resampling scheme developed in Dudek and Leśkow [6].

Słowa kluczowe

EN

bootstrap; consistency; multiplicative intensity model; periodic hazard function

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 3
• Strony: 229--251
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Dudek A.

• AGH University of Science and Technology Faculty of Applied Mathematics al. Mickiewicza 30, 30-059 Krakow, Poland,

Bibliografia

• [1] O. Aalen, Nonparametric Inference for a Family of Counting Processes, Ann. Statist. 6 (1978), 701–726.
• [2] P.K. Andersen, O. Borgan, R.D. Gill, N. Keiding, Statistical Models Based on Counting Processes, Springer, 1992.
• [3] W.J. Braun, R.J. Kulperger, A Bootstrap for Point Processes, J. Statist. Comput. Simul. 60 (1998), 129–155.
• [4] W.J. Braun, R.J. Kulperger, Re-Colouring the Intensity-Based Bootstrap for Point Processes, Commun. Stat. Simul. Comput. 32 (2003), 475–488.
• [5] A.C. Davison, D.V. Hinkley, Bootstrap Methods and Their Applications, Cambridge University Press, 1999.
• [6] A. Dudek, J. Leskow, Bootstrap algorithm in periodic multiplicative intensity model, to appear.
• [7] A. Dudek, M. Gocwin, J. Leskow (2008), Simultaneous Confidence Bands for the Integrated Hazard Function, Comput. Stat. 23 (1), 41–62.
• [8] P. Hall, C.C. Heyde, Martingale Limit Theory and Its Application, Academic Press, 1980.
• [9] A. Kwiecinski, R. Szekli, Some Monotonicity and Dependence Properties of Self-Exciting Point Processes, Ann. Appl. Probab. 6 (1996), 1211–1231.
• [10] S.N. Lahiri, Resampling Methods for Dependent Data, Springer, 2003.
• [11] J. Leskow, Histogram Maximum Likelihood Estimator of a Periodic Function in the Multiplicative Intensity Model, Stat. Decis. 6 (1988), 79–88.
• [12] J. Leskow, A Note on Kernel Smoothing of an Estimator of a Periodic Function in the Multiplicative Intensity Model, Stat. Probab. Lett. 7 (1989), 395–400.
• [13] J.M. Loh, M.L. Stein, Bootstrapping a Spatial Point Process, Stat. Sin. 14 (2004), 69–101.
• [14] D.N. Politis, J.P. Romano, A Circular Block-Resampling Procedure for Stationary Data. Exploring the Limits of Bootstrap, Edited by R. LePage and L. Billard, Wiley, New York, 1992, 263–270.
• [15] T. Rolski, R. Szekli, Stochastic Ordering and Thinning of Point Processes, Stoch. Proc. Appl. 37 (1991), 299–312.
• [16] J. Shao, D. Tu, The Jacknife and Bootstrap, Springer-Verlag, New York, 1995.