On a representation of fractional Brownian motion and the limit distributions of statistics arising in cusp statistical models

Preprint English OPEN
Kordzakhia, Nino; Kutoyants, Yury; Novikov, Alex; Hin, Lin-Yee;
(2017)
  • Subject: Mathematics - Statistics Theory
    arxiv: Mathematics::Probability

We discuss some extensions of results from the recent paper by Chernoyarov et al. (Ann. Inst. Stat. Math., October 2016) concerning limit distributions of Bayesian and maximum likelihood estimators in the model "signal plus white noise" with irregular cusp-type signals.... View more
  • References (18)
    18 references, page 1 of 2

    [12] Kim J., Pollard D. (1990) Cube root asymptotics. Ann. Stat., v.18, 191-219.

    [13] Kolmogorov, A. N. (1940). Wienersche Spiralen undeinige andere interessante Kurven im Hilbertschen Raum. C. R. (Doklady) Acad. Sci. URSS (N.S.), v.26, 115{118.

    [14] Kutoyants Yu. A. ( 1998) Statistical Inference for Spatial Poisson Processes, Lect. Notes Statist. v.134, Springer, New York.

    [15] Kutoyants, Y. (2004) Statistical Inference for Ergodic Di usion Processes. Springer Series in Statistics. Springer-Verlag London, Ltd., London.

    [16] Mandelbrot, B. and Van Ness, J.W. (1968) Fractional Brownian motions, fractional noises and applications. SIAM Rev. v.10, 422{437.

    [17] Muravlev, A. (2011) Representation of fractal Brownian motion in terms of an in nitedimensional Ornstein-Uhlenbeck process; translated from Uspekhi Mat. Nauk 66 (2011), no. 2(398), 235{236 Russian Math. Surveys 66, no. 2, 439{441.

    [18] Novikov, A. and Kordzakhia, N. (2013) Pitman estimators: an asymptotic variance revisited, SIAM Theory Probability and its Applications, v.57, N 3, 521-529.

    [19] Novikov, A., Kordzakhia, N. and Ling, T. (2014) On moments of Pitman estimators: the case of fractional Brownian motion, SIAM Theory Probability and its Applications, v.58, N. 4, 601-614.

    [20] P ug, G. (1982) Statistically important Gaussian process. Stochastic Process. Appl. 13, no. 1, 45{57.

    [21] Norros, I.; Valkeila, E.; Virtamo, J. (1999) An elementary approach to a Girsanov formula and other analytical results on fractional Brownian motions. Bernoulli, v.5, no. 4, 571{587.

  • Similar Research Results (4)
  • Metrics
Share - Bookmark