Method of Moments Estimators and Multi–step MLE for Poisson Processes

Ali S. Dabye1, Alix A. Gounoung1, Yury A. Kutoyants2
1Université Gaston Berger, Saint Louis, Sénégal
2Le Mans University, Le Mans, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

S. Albeverio, L.–J. Laob, X.–L. Zhaoc, Continuous Time Financial Market with a Poisson Process (Springer, New York, 2002.

I. Bar–David, “Communication under Poisson regime”, IEEETrans. Inform. Theory, IT–15 (1), 31–37, 1969.

P. Blasild, J. Granfeldt, Statistics with Applications in Biology and Geology (Chapman & Hall, London, 2003).

A.A. Borovkov, Mathematical Statistics (Gordon & Breach, Amsterdam, 1998).

R. Davies, “Testing the hypothesis that a point process is Poisson”, Adv. Appl. Probab., 9, 724–746, 1977.

I.A. Ibragimov, R. Z. Khasminskii, Statistical Estimation – Asymptotic Theory (Springer, New York, 1981).

K. Kamatani, M. Uchida, “Hybrid Multi–step estimators for stochastic differential equations based on sampled data”, Stat. Inference Stoch. Process, 18 (2), 177–204, 2015.

R. Z. Khasminskii, Yu. A. Kutoyants, “On parameter estimation of hidden telegraph process”, Bernoulli, 24 (3), 2064–2090, 2018.

Yu. A. Kutoyants, Parameter Estimation for Stochastic Processes (Heldermann, Berlin, 1984).

Yu. A. Kutoyants, Statistical Inference for Spatial Poisson Processes (Springer, New York, 1998)

Yu. A. Kutoyants, “On approximation of the backward stochastic differential equation. Small noise, large samples and high frequency cases”, Proc. Steklov Inst.Math., 287, 133–154, 2014.

Yu. A. Kutoyants, “On the Multi–step MLE–process for ergodic diffusion”, Stochastic Process. Appl., 127, 2243–2261, 2017.

Yu. A. Kutoyants Introduction to Statistics of Poisson Processes. To appear, 2019.

Yu. A. Kutoyants, “On approximation of BSDE and Multi–stepMLE–processes”, Probab. Uncertain.Quant. Risk., 1 (4), 23–41, 2016.

Yu. A. Kutoyants, A. Motrunich, “On Multi–step MLE–process for Markov sequences”, Metrika, 79 (6), 705–724, 2016.

L. Le Cam, “On the asymptotic theory of estimation and testing hypotheses”, Proc. 3rd Berkeley Symposium I, 355–368, 1956.

E.L. Lehmann, Elements of Large–Sample Theory (Springer, New York, 1999).

R. Liptser, A. N. Shiryayev, Statistics of Random Processes (Springer, New York, 2005).

S.E. Rigdon, A.P. Basu, Statistical Methods for the Reliability of Repairable Systems (JohnWiley, New York, 2000).

P.M. Robinson, “The stochastic difference between econometric statistics”, Econometrica, 56 (3), 531–548, 1988.

S.K. Sarkar, Single Molecule Biophysics and Poisson Process Approach to Statistical Mechanics (Morgan & Claypool, San Rafael CA, 2016).

D.R. Snyder,M.I.Miller, Random Point Processes in Time and Space (Springer, New York, 1991).

M. Uchida, N. Yoshida, “Adaptive estimation of ergodic diffusion process based on sampled data”, Stoch. Proces. Appl., 122, 2885–2924, 2012.

T.Utsu, Y. Ogata, R. Matsu’ura, “The centenary of the Omori formula for a decay law of aftershock activity”, J. Phys. Earth, 43, 1–33, 1995.