Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-17T01:34:10.032Z Has data issue: false hasContentIssue false
  • English
  • Français

The comparison of transient responses to stimuli

Published online by Cambridge University Press:  14 July 2016

Murray A. Cameron
Get access Rights & Permissions [Opens in a new window]

Abstract

In some experiments an ‘observation' is a time series and the ‘treatments' are stimuli which elicit changes in the nature of the time series for only a short period. One approach to analysing data from such experiments is presented here. Tests are given for detecting responses in such experiments, and for comparing responses elicited under different treatment regimes. The tests are based on frequency-domain estimates of the prediction variance for stationary time series. If several stimuli are applied within each observed time series at regular intervals, then the method of analysis may be designed so that the estimates of the different responses are orthogonal and most of the calculations can be performed using standard analysis of variance programs.

Keywords

ANALYSIS OF POWERFOURIER METHODSTIME SERIESTRANSIENTS
Type
Part 3—Hypothesis Testing and Distribution Theory for Time Series
Information
Journal of Applied Probability , Volume 23 , Issue A: Essays in Time Series and Allied Processes , 1986 , pp. 159 - 172
Copyright
Copyright © 1986 Applied Probability Trust 

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

Bennett, W. F. (1979) The analysis of transient spectral components with the autoregressive spectral estimator. Appl. Statist. 28, 1–13.CrossRefGoogle Scholar
Box, G. E. P. and Tiao, G. C. (1975) Intervention analysis with applications to economic and environmental problems. J. Amer. Statist. Assoc. 70, 70–79.CrossRefGoogle Scholar
Brillinger, D. R. (1973a) A power spectral estimate which is insensitive to transients. Technometrics 15, 559–562.CrossRefGoogle Scholar
Brillinger, D. R. (1973b) The analysis of time series collected in an experimental design. In Multivariate Analysis III, ed. Krishnaiah, P. R. Academic Press, New York, 241–256.Google Scholar
Brillinger, D. R. (1975) Time Series: Data Analysis and Theory. Holt, Rinehart and Winston, New York.Google Scholar
Brillinger, D. R. (1981) The general linear model in the design and analysis of evoked response experiments. J. Theoret. Neurobiol. 1, 105–119.Google Scholar
Cameron, M. A. (1978) The prediction variance and related statistics for stationary time series. Biometrika 65, 283–296.CrossRefGoogle Scholar
Cameron, M. A. and Hannan, E. J. (1979) Transient signals. Biometrika 66, 243–258.CrossRefGoogle Scholar
Jones, R. H., Crowell, D. H. and Kapuniai, L. E. (1970) Change detection model for serially correlated multivariate data. Biometrics 26, 269–280.CrossRefGoogle ScholarPubMed
Koopmans, L. H. (1974) The Spectral Analysis of Time Series. Academic Press, New York.Google Scholar
Mocks, J., Tuan, Pham Dinh and Gasser, T. (1984) Testing for homogeneity of noisy signals evoked by repeated stimuli. Ann. Statist. 12, 193–209.CrossRefGoogle Scholar
Tanaka, K. (1983) Estimation for transients in the frequency domain. J. Amer. Statist. Assoc. 78, 718–724.CrossRefGoogle Scholar
Tukey, J. W. (1977) Exploratory Data Analysis. Addison-Wesley, Reading, Mass.Google Scholar