On the robust estimation of power spectra, coherences, and transfer functions
- 10 January 1987
- journal article
- Published by American Geophysical Union (AGU) in Journal of Geophysical Research
- Vol. 92 (B1) , 633-648
- https://doi.org/10.1029/jb092ib01p00633
Abstract
Robust estimation of power spectra, coherences, and transfer functions is investigated in the context of geophysical data processing. The methods described are frequency‐domain extensions of current techniques from the statistical literature and are applicable in cases where section‐averaging methods would be used with data that are contaminated by local nonstationarity or isolated outliers. The paper begins with a review of robust estimation theory, emphasizing statistical principles and the maximum likelihood or M‐estimators. These are combined with section‐averaging spectral techniques to obtain robust estimates of power spectra, coherences, and transfer functions in an automatic, data‐adaptive fashion. Because robust methods implicitly identify abnormal data, methods for monitoring the statistical behavior of the estimation process using quantile‐quantile plots are also discussed. The results are illustrated using a variety of examples from electromagnetic geophysics.This publication has 37 references indexed in Scilit:
- Wigner-Ville spectral analysis of nonstationary processesIEEE Transactions on Acoustics, Speech, and Signal Processing, 1985
- Outlier-Induced CollinearitiesTechnometrics, 1985
- Exploring an Ozone Spatial Time Series in the Frequency DomainJournal of the American Statistical Association, 1985
- Least Median of Squares RegressionJournal of the American Statistical Association, 1984
- Exploratory data analysis in the geophysical sciencesReviews of Geophysics, 1980
- Electromagnetic Response Functions from Interrupted and Noisy DataJournal of geomagnetism and geoelectricity, 1980
- Confidence Interval Robustness with Long-Tailed Symmetric DistributionsJournal of the American Statistical Association, 1976
- A Robust Method for Multiple Linear RegressionTechnometrics, 1974
- Robust Estimation of a Location ParameterThe Annals of Mathematical Statistics, 1964
- Properties of sufficiency and statistical testsProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1937