Discrete-Time Spectral Estimation of Continuous-Time Processes - the Orthogonal Series Method (Spectral Estimation by Orthogonal Series).

摘要

Let X = (X(t), - infinity < t < infinity) be a stationary time series with spectral density function phi(lambda). Let (t sub n) be a stationary poisson point process on (- infinity, infinity), independent of X. The existence of consistent estimates of phi(lambda) based on the discrete-time observations (X(t sub n)), when the actual sampling instants (t sub n) are not known, has been an open question. Using an orthogonal series method, a class of spectral estimates is considered and its uniform and integratedly uniform consistency in quadratic mean is established. The rates of convergence are determined and compared with those of the kernel-type estimates based on the observations (X(t sub n), t sub n). (Author)