The Accuracy of Elemental Set Approximations for Regression

The elemental set algorithm involves performing many fits to a data set, each fit made to a subsample of size just large enough to estimate the parameters in the model. Elemental sets have been proposed as a computational device to approximate estimators in the areas of high breakdown regression and...

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Veröffentlicht in:Journal of the American Statistical Association Jg. 88; H. 422; S. 580 - 589
1. Verfasser: Hawkins, Douglas M.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria, VA Taylor & Francis Group 01.06.1993
American Statistical Association
Taylor & Francis Ltd
Schlagworte:
Algorithms
Approximation
Datasets
Diagnostics
Estimation methods
Estimators
Exact sciences and technology
High breakdown
Insect vectors
Linear inference, regression
Linear regression
Mathematical vectors
Mathematics
Outliers
Probability and statistics
Robust estimation
Sample mean
Sample size
Sciences and techniques of general use
Statistics
Theory and Methods
Outlier
Least squares method
Estimator robustness
Best estimation
Median
M estimation
Multiple regression
Elemental set method
Mean square error
ISSN:0162-1459, 1537-274X
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Beschreibung
Zusammenfassung:The elemental set algorithm involves performing many fits to a data set, each fit made to a subsample of size just large enough to estimate the parameters in the model. Elemental sets have been proposed as a computational device to approximate estimators in the areas of high breakdown regression and multivariate location/scale estimation, where exact optimization of the criterion function is computationally intractable. Although elemental set algorithms are used widely and for a variety of problems, the quality of the approximation they give has not been studied. This article shows that they provide excellent approximations for the least median of squares, least trimmed squares, and ordinary least squares criteria. It is suggested that the approach likely will be equally effective in the other problem areas in which exact optimization of a criterion is difficult or impossible.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1993.10476310