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On estimation in the multiplicative intensity model via histogram sieve

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Języki publikacji
EN
Abstrakty
EN
In the paper we consider the problem of estimating stochastic intensity of a point process from multiplicative intensity model using the method of sieves of Grenander [6]. Basic properties of the histogram sieve estimator including consistency and asymptotic normality are proved. Our approach extends results obtained in Leśkow and Różański [13].
Rocznik
Strony
89--99
Opis fizyczny
Bibliogr. 19 poz., tab., wykr.
Twórcy
  • Institute of Mathematics, Wrocław University of Technology, 50-370 Wroclaw, Poland
  • Institute of Mathematics, Wrocław University of Technology, 50-370 Wroclaw, Poland
Bibliografia
  • [1] O. Aalen, Nonparametric inference for a family of counting processes, Ann. Statist. 6 (4) (1978), pp. 701-726.
  • [2] P. Andersen, O. Borgan, R. Gill and N. Keiding, Statistical Models Based on Counting Processes, Springer, New York 1993.
  • [3] P. K. Andersen and O. Borgan, Counting process models for life history, Scand. J. Statist. 12 (1985), pp. 97-158.
  • [4] P. Billingsley, Convergence of Probability Measures, Wiley, 1968.
  • [5] M. Feinleib, A method of analyzing log normally distributed survival data with incomplete follow-up, J. Amer. Statist. Assoc. 55 (1960), pp. 534-545.
  • [6] U. Grenander, Abstract Inference, Wiley, New York 1981.
  • [7] R. D. Horner, Age at onset of Alzheimer’s disease: Clue to the relative importance of etiologie factors'? Amer. J. Epidemiology 126 (1987), pp. 409-414.
  • [8] A. F. Karr, Point Processes and Their Statistical Inference, M. Dekker Inc., New York 1986.
  • [9] J. P. Klein and M. L. Moeschberger, Survival Analysis: Techniques for Censored and Truncated Data, Springer, New York 1998.
  • [10] J. Leśkow, Histogram maximum likelihood estimator of a periodic function in the multiplicative intensity model, Statist Decisions 6 (1988), pp. 79-88.
  • [11] J. Leśkow, A note on a kernel regularization of a histogram estimator in the multiplicative intensity model Statist. Probab. Lett. 7 (1989), pp. 395-400.
  • [12] J. Leśkow, Sieve-based maximum likelihood estimator for almost periodic stochastic processes models, Probab. Math. Statist. 14 (1) (1993), pp. 11-24.
  • [13] J. Leśkow and R. Różański, Histogram maximum likelihood estimator in the multiplicative intensity model, Stochastic Process. Appl. 31 (1989), pp. 151-159.
  • [14] R. Liptser and A. Shiryayev, Statistics of Random Processes, Polish edition, Warszawa 1981.
  • [15] B. L. S. Prakasa Rao, Semimartingale and Their Statistical Inference, Chapman 1999.
  • [16] H. Ramlau-Hansen, Smoothing counting process intensities by means of kernel function, Ann. Statist. 11 (1983), pp. 453-466.
  • [17] R. Rebolledo, Central limits theorems for local martingales, Z. Wahrscheinlichkeitstheorie verw. Gebiete 51 (1980), pp. 269-286.
  • [18] F. Topsøe, On the connection between P-continuity and P-uniformity in weak convergence, Teor. Veroyatnost. i Primenen. 12 (2) (1967), pp. 279-288.
  • [19] W. Weibull, A statistical distribution of wide applicability, J. Appl. Mech. 18 (1951), pp. 293-297.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-83cf79be-c166-4c95-a1ec-95c0724b0cc7
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