Nonparametric inference for Markovian interval processes

Stochastic Processes and their Applications

Volumn 67, Issue 1, 1997, Pages 1-23

  Utikal, Klaus J ^a  

^a UNIVERSITY OF BONN   (Germany)

Author keywords

Counting process regression; Goodness of fit test; Hazard estimation; Intensity; Kernel function smoothing; Markov process; Martingale central limit theorem; Neuronal spike trains; Nonparametric functional estimation; Renewal process

Indexed keywords

EID: 0031589121     PISSN: 03044149     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-4149(96)00129-9     Document Type: Article

References (24)

1. O. Aalen. Nonparametric inference for a family of counting processes, Ann. Statist. 6 (1978) 701 726.
2. P.K. Andersen and Ø. Borgan and R.D. Gill and N. Keiding. Statistical Models Based on Counting Processes (Springer, New York, 1992).
3. E. Arjas and P. Haara and R. Tweedie. A system model with interacting components: renewal type results. Optimization 16 (1985) 297-311.
4. A. Arms and P.S. Camp, Biology: A Journey into Life (W.B. Saunders, New York, 1988).
5. P. Billingsley. Convergence of Probability Measures (Wiley, New York, 1968).
6. G.N. Borisyuk, R.N. Borisyuk, A.B. Kirillov, E.I. Kovalenko and V.I. Kryukov. A new statistical method for identifying interconnections between neuronal network elements, Biol. Cybernet. 52 (1985) 301-306.
7. D.R. Brillinger. Nerve cell spike train data analysis: a progression of technique, J. Amer. Statist. Assoc. K7 (1992) 260-271.
8. E.S. Chornoboy, L.P. Schramm and A.F. Karr. Maximum likelihood identification of neural point process system, Biol. Cybernat 59 (1988) 265-275.
9. D.R. Cox. Regression models and life-tables (with discussion), J. Roy. Statist. Soc. Ser. B 34 (1972) 187-220.
10. D.R. Cox and P.A.W. Lewis, Multivariate point processes. Proc. 6th Berkeley Symp. Math. Statist. Probab., Vol. 3 (1972) 401-448.
11. D.J. Daley and D. Vere-Jones. An Introduction to the Theory of Point Processes (Springer, New York. 1988).
12. J. Doob, Stochastic Processes (Wiley, New York. 1953).
13. M.K. Habib and P.K. Sen. Non-stationary stochastic point-process models in neurophysiology with applications to learning and memory. in: Biostatistics: Statistics in Biomedical. Public Health and Environmental Sciences (Eisevier. North-Holand, 1985) 481-509.
14. B.G. Lindsey, Y.M. Hernandez, D.F. Morris and R. Shannon. Functional connectivity between brain stem midline neurons with respiratory-modulated firing rates. J. Neurophysiol. 67 (1992) 890-904.
15. I.W. McKeague and K.J. Utikal. Identifying nonlinear covariate effects in semi-martingale regression models. Probab. Theory Related Fields 11 (1990) 1-25.
16. I.W. McKeague and K.J. Utikal. Goodness-of-fit tests for additive hazards and proportional hazard models, Scand. J. Statist. 18 (1991) 177-195.
17. D.H. Perkel, G.L. Gerstein and G.P. Moore. Neuronal spike trains and stochastic point process. ii. simultaneous spike trains. Biophys, J. (1967) 419-440.
18. R. Rebolledo. Central limit theorems for local martingales. Z. Wahrscheinlichkeitsthcor. Verw. Geb. 51 (1980) 269-286.
19. E. Slud. Multivariate dependent renewal processes, Adv. Appl. Probab. 16 (1984) 347-362.
20. K.J. Utikal. Markovian interval processes i: nonparametric inference. Tech. Rept. No. 347, Dept. of Statistics. Univ. Kentucky (1994a).
21. K.J. Utikal. Semiparametric inference on neural connectivity. Tech. Rept. No. 350. Dept. of Statistics. Univ. Kentucky (1994b).
22. K.J. Utikal. A nonparametric method for detecting neural connectivity. Proc. 10th Internat. Workshop on Statistical Modeling (1995a).
23. K.J. Utikal. A new method for detecting neural interConnectivity, to appear in: Biol. Cybernet (I995b).
24. K.J. Utikal. Markovian interval processes I: nonparametric inference. Discussion paper No. A-486. Wirtschaftstheorie II. Universität Bonn (1995c).