The estimation of frequency

Journal of Applied Probability - Tập 10 Số 3 - Trang 510-519 - 1973
E. J. Hannan1
1The Australian National University

Tóm tắt

Very general forms of the strong law of large numbers and the central limit theorem are proved for estimates of the unknown parameters in a sinusoidal oscillation observed subject to error. In particular when the unknown frequency θ0, is in fact 0 or <it is shown that the estimate, , satisfies for N ≧ N0 (ω) where N0 (ω) is an integer, determined by the realisation, ω, of the process, that is almost surely finite.

Từ khóa


Tài liệu tham khảo

Whittle, 1959, Sur la distribution du maximum d'un polynome trigonométrique à coefficients aléatoires, Colloques Internationaux du Centre National de la Recherche Scientifique, 87, 173

Hannan E. J. (1973) Central limit theorems for time series regression. Zeit. Wahrscheinlichkeitsth. 14.

10.1017/S0021900200114664

10.1214/aoms/1177693494

Jirina, 1958, Stochastic branching processes with continuous state space, Czech. Math. J., 8, 292, 10.21136/CMJ.1958.100304

10.1002/9780470316429

Ibragimov, 1971, Independent and Stationary Sequences of Random Variables

Doob, 1953, Stochastic Processes

10.1093/biomet/58.1.21

Thông tin
Thông tin xuất bản

Journal of Applied Probability

Tập 10 Số 3

510-519

Thông tin tác giả