Journal article
Calculating the Breakdown Point of Sparse Linear Models
Technometrics, Vol.51(1), pp.34-46
02/01/2009
DOI: 10.1198/TECH.2009.0004
Abstract
In robust statistics, the concept of breakdown point was introduced to quantify the robustness of an estimator in a linear regression model. Computing the breakdown point is useful in tuning some robust regression estimators (e.g., the least trimmed squares estimator). Computing the breakdown point for a structured linear model (i.e., one with dependencies among some p rows of the n × p design matrix X) can be very demanding. This article presents an algorithm for calculating the maximum breakdown point for sparse linear models, which are a special type of structured linear model whose design matrix has many zero entries. The algorithm decomposes a sparse design matrix into smaller submatrixes on which the computation is performed, thereby leading to substantial savings in computation. An assembly process, along with a few numerical examples, illustrate the application of the algorithm and demonstrate its computational benefits.
Details
- Title: Subtitle
- Calculating the Breakdown Point of Sparse Linear Models
- Creators
- Jung Jin ChoYong ChenYu Ding
- Resource Type
- Journal article
- Publication Details
- Technometrics, Vol.51(1), pp.34-46
- Publisher
- Taylor & Francis
- DOI
- 10.1198/TECH.2009.0004
- ISSN
- 0040-1706
- eISSN
- 1537-2723
- Language
- English
- Date published
- 02/01/2009
- Academic Unit
- Industrial and Systems Engineering
- Record Identifier
- 9984064222602771
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