Estimating a periodicity parameter in the drift of a time inhomogeneous diffusion

Reinhard Höpfner1, Yury A. Kutoyants2
1Inst. Math., Univ. Mainz, Mainz, Germany
2Laborat. Statist. et Process., Univ. Maine, Mainz, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

N. Bingham, C. Goldie, and J. Teugels, Regular Variation (Cambridge, 1987).

C. Brandt, Partial Reconstruction of the Trajectories of a Discretely Observed Branching Diffusion with Immigration and an Application to Inference, PhD thesis (Universität Mainz, 2005).

I. Castillo, C. Lévy-Leduc, and C. Matias, “Exact Adaptive Estimation of the Shape of a Periodic Function with Unknown Period Corrupted by White Noise,” Math. Methods Statist. 15, 1–30 (2006).

S. Dachian, “On Limiting Likelihood Ratio Processes of Some Change-Point Type Statistical Models”, J. Statist. Plann. Inference 140, 2682–2692 (2010).

R. Davies, “Asymptotic Inference when the Amount of Information is Random”, in: Proc. of the Berkeley Symposium in Honour of J. Neyman and J. Kiefer, Ed. by L. Le Cam and R. Olshen (Wadsworth, 1985), Vol. II.

H. Dehling, B. Franke, and T. Kott, “Drift Estimation for a Periodic Mean Reversion Process”, Statist. Inference Stoch. Proc. 13, 175–192 (2010).

J. Deshayes and D. Picard, “Lois asymptotiques des tests et estimateurs de rupture dans un modèle statistique classique”, Ann. Inst. H. Poincaré B 20, 309–327 (1984).

G. Golubev, “Computation of Efficiency of Maximum-Likelihood Estimate when Observing a Discontinuous Signal in White Noise”, Problems Inform. Transmission 15, 61–69 (1979).

G. Golubev, “Estimating the Period of a Signal of Unknown Shape Currupted by White Noise”, Problems Inform. Transmission 24, 38–52 (1988).

J. Hájek, “A Characterization Theorem of Limiting Distributions for Regular Estimators”, Z. Wahrsch. verw. Geb. 14, 323–330, 1970.

J. Hájek and Z. Šidák, Theory of Rank Tests (Academic Press, 1967).

R. Höpfner and Y. Kutoyants, “Estimating Discontinuous Periodic Signals in a Time-Inhomogeneous Diffusion”, Statist. Inference Stoch. Proc. 13, 193–230 (2010).

R. Höpfner and Y. Kutoyants, “On LAN for Parametrized Continuous Periodic Signals in a Time-Inhomogeneous Diffusion”, Statistics & Decisions 27, 309–326 (2010).

I. Ibragimov and R. Hasminskii, Statistical Estimation: Asymptotic Theory (Springer, 1981).

N. Ikeda and S. Watanabe, Stochastic Differential Equations and Diffusion Processes. 2nd ed. (North-Holland/Kodansha, 1989).

J. Jacod and A. Shiryaev, Limit Theorems for Stochastic Processes (Springer, 1987).

J. Karatzas and S. Shreve, Brownian Motion and Stochastic Calculus, 2nd ed. (Springer, 1991).

U. Küchler and Y. Kutoyants, “Delay Estimation for Some Stationary Diffusion-Type Processes”, Scand. J. Statist. 27, 405–414 (2000).

Y. Kutoyants, Statistical Inference in Spatial Poisson Processes, in Springer Lect. Notes Math. (Springer, 1998), Vol. 134.

Y. Kutoyants, Statistical Inference for Ergodic Diffusion Processes (Springer, 2004).

L. Le Cam, Théorie asymptotique de la décision statistique (Univ. Montréal, 1969).

L. Le Cam and G. Yang, Asymptotics in Statistics. Some Basic Concepts (Springer, 1990), 2nd ed. (Springer, 2002).

F. Liese and K. Miescke, Statistical Decision Theory (Springer, 2008).

R. Liptser and A. Shiryaev, Statistics of Random Processes (Springer, 1981), 2nd ed. (Springer, 2001), Vols. I, II.

J. Pfanzagl, Parametric Statistical Inference (de Gruyter, 1994).

H. Rubin and K. Song, “Exact Computation of the Asymptotic Efficiency of Maximum Likelihood Estimators of a Dicontinuous Signal in a Gaussian White Noise”, Ann. Statist. 23, 732–739 (1995).

H. Strasser, Mathematical Theory of Statistics (de Gruyter, 1985).

A. van der Vaart, Asymptotic Statistics (Cambridge, 1998).

H. Witting and U. Müller-Funk, Mathematische Statistik (Teubner, 1995), Vol. II.