Robust frequency estimation using elemental sets

Smyth, Gordon K. and Hawkins, Douglas M. (2000) Robust frequency estimation using elemental sets. Journal of Computational and Graphical Statistics, 9 1: 196-214. doi:10.2307/1390621


Author Smyth, Gordon K.
Hawkins, Douglas M.
Title Robust frequency estimation using elemental sets
Journal name Journal of Computational and Graphical Statistics   Check publisher's open access policy
ISSN 1061-8600
1537-2715
Publication date 2000-03
Sub-type Article (original research)
DOI 10.2307/1390621
Volume 9
Issue 1
Start page 196
End page 214
Total pages 19
Editor Andreas Buja
Place of publication Alexandria, VA, U.S.A.
Publisher American Statistical Association; Institute of Mathematical Statistics; Interface Foundation of North America
Collection year 2000
Language eng
Subject C1
230203 Statistical Theory
780101 Mathematical sciences
Formatted abstract
The extraction of sinusoidal signals from time-series data is a classic problem of ongoing interest in the statistics and signal processing literatures. Obtaining least squares estimates is difficult because the sum of squares has local minima O(1/𝑛) apart in the frequencies. In practice the frequencies are often estimated using ad hoc and inefficient methods. Problems of data quality have received little attention. An elemental set is a subset of the data containing the minimum number of points such that the unknown parameters in the model can be identified. This article shows that, using a variant of the classical method of Prony, parameter estimates for a sum of sinusoids can be obtained algebraically from an elemental set. Elemental set methods are used to construct finite algorithm estimators that approximately minimize the least squares, least trimmed sum of squares, or least median of squares criteria. The elemental set estimators prove able in simulations to resolve the frequencies to the correct local minima of the objective functions. When used as the first stage of an MM estimator, the constructed estimators based on the trimmed sum of squares and least median of squares criteria produce final estimators which have high breakdown properties and which are simultaneously efficient when no outliers are present. The approach can also be applied to sums of exponentials, and sums of damped sinusoids. The article includes simulations with one and two sinusoids and two data examples.
© 2000 American Statistical Associatian, Institute of Mathematical Statistics, and Interface Foundation of North America.
Keyword Statistics & Probability
High Breakdown
High Efficiency
Least Median Of Squares
Least Trimmed Sum Of Squares
Mm Estimators
Sums Of Exponential Functions
Modified Prony Algorithm
Nonlinear-regression
Breakdown
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
 
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Created: Tue, 10 Jun 2008, 10:22:35 EST