Estimating functionals of one-dimensional Gibbs states
Tóm tắt
Some estimators of maximum likelihood type are constructed for estimating functionals of one-dimensional Gibbs states. We also show that those estimators are strongly consistent, asymptotically normal and asymptotically efficient.
Tài liệu tham khảo
Bowen, R.: Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lecture Notes in Math. 470. berlin Heidelberg New York: Springer 1975
Ibragimov, I.A., Has'minskii, R.Z.: Statistical estimation-asymptotic theory. Berlin Heidelberg New York: Springer 1981
Ji, C.: Estimating functionals of one-dimensional Gibbs states. Technical Report 87-33, Department of Statistics, Purdue University (1987)
Kato, T.: Perturbation theory for linear operators, 2nd ed. Berlin Heidelberg New York: Springer 1976
Kedem, B.: Binary time series. Lect. Notes Pure Appl. Math. 52. New York: Marcel Dekker 1980
Koshevnik, Y.A., Levit, B.Y.: On a non-parametric analogue of the information matrix. Theory Probab. Appl.4, 738–753 (1976)
Lalley, S.P.: Ruelle's Perron-Frobenius theorem and the central limit theorem for additive functionals of one-dimensional Gibbs states. Proc. Conf. in Honor of H. Robbins (1985)
Lalley, S.P.: Distribution of periodic orbits of symbolic and axiom A flows. Adv. Appl. Math.8, 154–193 (1987)
Ripley, B.D.: Spatial statistics. New York: John Wiley and Sons 1981
Ruelle, D.: Thermodynamic formalism. Reading, Massachusetts: Addison-Wesley 1978
Stein, C.: Efficient non-parametric testing and estimation. Proc. Third Berkeley Sympos., Math. Stat. Probab.1, 187–195 (1956)