On invariant density estimation for ergodic difusion processes

• Autores: Yury A. Kutoyants
• Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 28, Nº. 2, 2004, págs. 111-124
• Idioma: inglés
• Títulos paralelos:
  • Estimación de densidad invariante para procesos de difusión ergódica.
• Enlaces
  • Texto completo (pdf)
• Resumen
  • català

    Presentem una revisi¿o d'alguns resultats sobre estimaci¿o invariant de densitats per observacions de processos de difusi¿o erg`odics, i alguns problemes relacionats. Per a cada problema proposem una cota inferior minimax sobre els riscos de tots els estimadors i aleshores constru¿im un estimador asimpt`oticament eficient. Aquest treball va ser presentat a la Barcelona Conference on Asymptotic Statistics, celebrada a Bellaterra (Barcelona, 2003).

  • English

    We present a review of several results concerning invariant density estimation by observations of ergodic diffusion process and some related problems. In every problem we propose a lower minimax bound on the risks of all estimators and then we construct an asymptotically efficient estimator. This contribution has been presented in the Barcelona Conference on Asymptotic Statistics, which took place in Bellaterra (Barcelona, 2003).

• Referencias bibliográficas
  • Banon, G. (1978). Non parametric identification for diffusion processes.SIAM. J. Control Optim., 16, 3, 380-395.
  • Bosq, D., Davydov, Y. (1998). Local time and density estimation in continuous time.Math. Methods Statist., 8, 1, 22-45.
  • Bosq, D. (1998).Nonparametric Statistics for Stochastic Processes.(Second edition), Lecture Notes Statist., 110, New York: Springer-Verlag.
  • Castellana, J. V., Leadbetter, M. R. (1986). On smoothed density estimation for stationary processes. Stochastic Process. Appl., 21, 179-193.
  • Dalalyan, A. (2002). Sharp adaptive estimation of the trendcoefficient for ergodic diffusion, preprint n.o 02-1, Laboratoire Statistique et...
  • Dalalyan, A., Kutoyants, Yu. A. (2002). Asymptotically efficient trend coefficient estimation for ergodic diffusion.Math. Methods Statist.,...
  • Dalalyan, A., Kutoyants, Yu. A. (2003). Asymptotically efficient estimation of the derivative of invariant density.Stat. Inference Stoch....
  • Dalalyan, A., Kutoyants, Yu. A. (2004). On second order minimax estimation of invariant density for ergodic diffusion.Statistics& Decisions,...
  • Dehay, D., Kutoyants, Yu. A. (2004). On confidence intervalsfor distribution function and density of ergodic diffusion process.J. Statist....
  • Delecroix, M. (1980). Sur l’estimation des densités d’un processus stationnairèa temps continu. Publications de l’ISUP, XXV, 1-2, 17-39.
  • Durett, R. (1996).Stochastic Calculus: A Practical Introduction. Boca Raton: CRC Press.
  • Galtchouk, L. and Pergamenshchikov, S. (2001). Sequentialnonparametric adaptive estimation of the drift coefficient in diffusion processes.Math....
  • Golubev, G. K., Levit, B. Ya. (1996). On the second order minimax estimation of distribution functions. Math. Methods Statist., 5, 1, 1-31.
  • Ibragimov, I. A., Khasminskii, R. Z. (1981).Statistical Estimation. Asymptotic Theory.New York: Springer-Verlag.
  • Karatzas, I., Shreve, S. E. (1991).Brownian Motion and Stochastic Calculus.New York: Springer-Verlag.
  • Kutoyants, Yu. A. (1997a). Efficiency of empiric distribution function for ergodic diffusion processes. Bernoulli, 3 (4), 445-456.
  • Kutoyants, Yu. A. (1997b). Some problems of nonparametric estimation by the observations of ergodic diffusion processes.Statist. Probab. Lett.,32,...
  • Kutoyants Yu. A. (1997c). On semiparametric estimation for ergodic diffusion.Proc. A. Razmadze Math. Inst. (in honor of R. Chitashvili), Tbilisi,...
  • Kutoyants, Yu. A. (1997d). On density estimation by the observations of ergodic diffusion processes. In Statistics and Control of Stochastic...
  • Kutoyants, Yu. A. (1998). Efficient density estimation for ergodic diffusion process.Stat. Inference Stoch. Process., 1, 2, 131-155.
  • Kutoyants, Yu. A. (2003).Statistical Inference for Ergodic Diffusion Processes. New York: Springer.
  • Kutoyants, Yu. A., Negri, I. (2001). OnL2 efficiency of empiric distribution of ergodic diffusion processs. Theory Probab. Appl., 46, 1, 164-169.
  • Negri, I. (2001). On efficient estimation of invariant density for ergodic diffusion processes.Statist. Probab. Lett., 51, 1, 79-85.
  • Nguyen, H. T. (1979). Density estimation in a continuous-time Markov processes.Ann. Statist., 7, 341-348.
  • Pinsker, M. S. (1980). Optimal filtering of square integrable signals in Gaussian white noise.Probl. Inf. Transm., 16, 120-133.
  • Veretennikov, A. Yu. (1999). On Castellana-Leadbetter’s condition for diffusion density estimation.Stat. Inference Stoch. Process., 2, 1,...
  • van Zanten, H. (2001). Rates of convergence and asymptotic normality of kernel estimators for ergodic diffusion processes.Nonparametric Statist.,...