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September, 1980 Discrete-Time Spectral Estimation of Continuous-Time Processes-The Orthogonal Series Method
E. Masry
Ann. Statist. 8(5): 1100-1109 (September, 1980). DOI: 10.1214/aos/1176345147

Abstract

Let $\{X(t), - \infty < t < \infty\}$ be a stationary time series with spectral density function $\phi(\lambda).$ Let $\{t_n\}$ be a stationary Poisson point process on the real line. The existence of consistent estimates of $\phi(\lambda)$ based on the discrete-time observations $\{X(t_n)\}^N_{n = 1},$ when the actual sampling times are not known, has been an open question (Beutler). Using an orthogonal series method, a class of spectral estimates is considered and its uniform and integrated uniform consistency in quadratic mean is established. Rates of convergence are established and are compared with the optimal rates of the available (Brillinger, Masry) kernel-type estimates based on the observations $\{X(t_n), t_n\}^N_{n = 1}$.

Citation

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E. Masry. "Discrete-Time Spectral Estimation of Continuous-Time Processes-The Orthogonal Series Method." Ann. Statist. 8 (5) 1100 - 1109, September, 1980. https://doi.org/10.1214/aos/1176345147

Information

Published: September, 1980
First available in Project Euclid: 12 April 2007

zbMATH: 0445.62104
MathSciNet: MR585708
Digital Object Identifier: 10.1214/aos/1176345147

Subjects:
Primary: 62M15

Keywords: Convergence rates , orthogonal series estimates , spectral estimation

Rights: Copyright © 1980 Institute of Mathematical Statistics

Vol.8 • No. 5 • September, 1980
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