Hostname: page-component-89b8bd64d-sd5qd Total loading time: 0 Render date: 2026-05-07T08:51:31.628Z Has data issue: false hasContentIssue false
  • English
  • Français

Non-parametric covariance estimation from irregularly-spaced data

Published online by Cambridge University Press:  01 July 2016

Elias Masry
Elias Masry*
Affiliation:
University of California at San Diego
*
∗Postal address: Department of Electrical Engineering and Computer Sciences, Mail Code C-014, University of California, San Diego, La Jolla, CA 92093, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Abstract

The non-parametric discrete-time estimation of the covariance function R(t) of stationary continuous-time processes is considered. The characteristics of the sampling instants necessary for the consistent estimation of R(t) are explored. A class of covariance estimates is introduced and its asymptotic statistics are derived.

Keywords

DETERMINISTIC AND RANDOM SAMPLING SCHEMESPOISSON POINT PROCESSQUADRATIC-MEAN CONSISTENCYCONVERGENCE RATESASYMPTOTIC NORMALITY

Information

Type
Research Article
Information
Advances in Applied Probability , Volume 15 , Issue 1 , March 1983 , pp. 113 - 132
Copyright
Copyright © Applied Probability Trust 1983 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

This work was supported by the Office of Naval Research under Contract N000 14-75-C-0652.

References

Beutler, F. J. and Leneman, O. A. Z. (1966) The theory of stationary point processes. Acta Math. 116, 159–197.CrossRefGoogle Scholar
Brillinger, D. R. (1972) The spectral analysis of stationary interval functions. Proc. 6th Berkeley Symp. Math. Statist. Prob. 1, 483–513.Google Scholar
Brillinger, D. R. (1975) Time Series Data Analysis and Theory. Holt, Rinehart and Winston, New York.Google Scholar
Daley, D. J. and Vere-Jones, D. (1972) A summary of the theory of point processes. In Stochastic Point Processes, ed. Lewis, P. A. W., Wiley, New York, 299–383.Google Scholar
Doob, J. L. (1948) Renewal theory from the point of view of the theory of probability. Trans. Amer. Math. Soc. 63, 422–438.CrossRefGoogle Scholar
Durranti, T. S. and Greated, C. A. (1977) Laser Systems in Flow Measurements. Plenum, New York.CrossRefGoogle Scholar
Gaster, M. and Roberts, J. B. (1975) Spectral analysis of randomly sampled signals. J. Inst. Math. Appl. 15, 195–216.CrossRefGoogle Scholar
McDunnough, P. and Wolfson, D. B. (1979) On some sampling schemes for estimating the parameters of a continuous-time series. Ann. Inst. Statist. Math. 31, 487–497.CrossRefGoogle Scholar
Masry, E. (1978a) Poisson sampling and spectral estimation of continuous-time processes. IEEE Trans. Information Theory 24, 173–183.CrossRefGoogle Scholar
Masry, E. (1978b) Alias-free sampling: An alternative conceptualization and its applications. IEEE Trans. Information Theory 24, 317–324.CrossRefGoogle Scholar
Masry, E. (1980) Discrete-time spectral estimation of continuous-time processes–the orthogonal series method. Ann. Statist. 5, 1100–1109.Google Scholar
Parzen, E. (1967) Time Series Analysis Papers. Holden-Day, San Francisco.Google Scholar
Robinson, P. M. (1977) Estimation of a time series from unequally spaced data. Stoch. Proc. Appl. 6, 9–24.CrossRefGoogle Scholar
Shapiro, H. S. and Silverman, R. A. (1960) Alias-free sampling of random noise. J. SIAM 8, 225–248.Google Scholar