Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-04T05:16:31.110Z Has data issue: false hasContentIssue false
  • English
  • Français

The signal-noise problem — a solution for the case that signal and noise are Gaussian and independent

Published online by Cambridge University Press:  14 July 2016

Michael F. Driscoll
Michael F. Driscoll*
Affiliation:
Arizona State University
Get access Rights & Permissions [Opens in a new window]

Abstract

A solution is obtained for the signal-noise problem X = M + Z in which M and Z are independent Gaussian processes. Conditions on the processes are given which insure that the best estimate under generalized square — error loss is the conditional mean of M given X = x. A sequence of approximators of the best estimate is also given.

Keywords

SIGNAL-NOISE PROBLEMGAUSSIAN PROCESSESREPRODUCING KERNEL HILBERT SPACES
Type
Short Communications
Information
Journal of Applied Probability , Volume 12 , Issue 1 , March 1975 , pp. 183 - 187
Copyright
Copyright © Applied Probability Trust 1975 

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.)

References

[1] Aronszajn, N. (1950) Theory of reproducing kernels. Trans. Amer. Math. Soc. 68, 337–404.Google Scholar
[2] Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
[3] Driscoll, M. F. (1971) Estimation of the mean value function of a Gaussian process . Ph.D. dissertation, University of Arizona.Google Scholar
[4] Driscoll, M. F. (1973) The reproducing kernel Hilbert space structure of the sample paths of a Gaussian process. Z. Wahrscheinlichkeitsth. 26, 309–316.Google Scholar
[5] Loeve, M. (1963) Probability Theory (3rd. ed.). Van Nostrand, Priceton, N. J. Google Scholar
[6] Parzen, E. (1959) Statistical Inference on Time Series by Hilbert Space Methods, I. Dept. of Statist., Stanford Univ., Technical Report No. 23, January 2, 1959.Google Scholar
[7] Parzen, E. (1963) Probability density functionals and reproducing kernel Hilbert spaces. Time Series Analysis. Rosenblatt, M., Ed. Wiley, New York. 155–169.Google Scholar