The University of Southampton
University of Southampton Institutional Repository

Optimization techniques for multivariate least trimmed absolute deviation estimation

Optimization techniques for multivariate least trimmed absolute deviation estimation
Optimization techniques for multivariate least trimmed absolute deviation estimation
Given a dataset an outlier can be defined as an observation that it is unlikely to follow the statistical properties of the majority of the data. Computation of the location estimate of is fundamental in data analysis, and it is well known in statistics that classical methods, such as taking the sample average, can be greatly affected by the presence of outliers in the data. Using the median instead of the mean can partially resolve this issue but not completely. For the univariate case, a robust version of the median is the Least Trimmed Absolute Deviation (LTAD) robust estimator introduced in [18], which has desirable asymptotic properties such as robustness, consistently, high breakdown and normality. There are different generalizations of the LTAD for multivariate data, depending on the choice of norm. In [5] we present such a generalization using the Euclidean norm and propose a solution technique for the resulting combinatorial
optimization problem, based on a necessary condition, that results in a highly convergent local search algorithm. In this subsequent work we use the L1 norm to generalize the LTAD to higher dimensions, and show that the resulting mixed integer programming problem has an integral relaxation, after applying an appropriate data transformation. Moreover, we utilize the structure of the problem to show that the resulting LP’s can be solved efficiently using a subgradient optimization approach. The robust statistical properties of the proposed estimator are verified by extensive computational results.
Zioutas, G.
7a252159-4ebb-4a4c-95cd-977ca6f37782
Chatzinakos, C
284611a3-35e1-43bb-8c32-8fb9e053920c
Nguyen, T.-D.
a6aa7081-6bf7-488a-b72f-510328958a8e
Pitsoulis, L.
daf78d54-b152-487e-b343-e50c43452fca
Zioutas, G.
7a252159-4ebb-4a4c-95cd-977ca6f37782
Chatzinakos, C
284611a3-35e1-43bb-8c32-8fb9e053920c
Nguyen, T.-D.
a6aa7081-6bf7-488a-b72f-510328958a8e
Pitsoulis, L.
daf78d54-b152-487e-b343-e50c43452fca

Zioutas, G., Chatzinakos, C, Nguyen, T.-D. and Pitsoulis, L. (2017) Optimization techniques for multivariate least trimmed absolute deviation estimation. Journal of Combinatorial Optimization. (doi:10.1007/s10878-017-0109-1).

Record type: Article

Abstract

Given a dataset an outlier can be defined as an observation that it is unlikely to follow the statistical properties of the majority of the data. Computation of the location estimate of is fundamental in data analysis, and it is well known in statistics that classical methods, such as taking the sample average, can be greatly affected by the presence of outliers in the data. Using the median instead of the mean can partially resolve this issue but not completely. For the univariate case, a robust version of the median is the Least Trimmed Absolute Deviation (LTAD) robust estimator introduced in [18], which has desirable asymptotic properties such as robustness, consistently, high breakdown and normality. There are different generalizations of the LTAD for multivariate data, depending on the choice of norm. In [5] we present such a generalization using the Euclidean norm and propose a solution technique for the resulting combinatorial
optimization problem, based on a necessary condition, that results in a highly convergent local search algorithm. In this subsequent work we use the L1 norm to generalize the LTAD to higher dimensions, and show that the resulting mixed integer programming problem has an integral relaxation, after applying an appropriate data transformation. Moreover, we utilize the structure of the problem to show that the resulting LP’s can be solved efficiently using a subgradient optimization approach. The robust statistical properties of the proposed estimator are verified by extensive computational results.

Text
LPLTAD - Accepted Manuscript
Download (156kB)

More information

Accepted/In Press date: 10 January 2017
e-pub ahead of print date: 25 January 2017
Organisations: Operational Research

Identifiers

Local EPrints ID: 406194
URI: http://eprints.soton.ac.uk/id/eprint/406194
PURE UUID: a11869ec-0a5e-4452-8e93-4e5b799813ba
ORCID for T.-D. Nguyen: ORCID iD orcid.org/0000-0002-4158-9099

Catalogue record

Date deposited: 10 Mar 2017 10:41
Last modified: 16 Mar 2024 05:06

Export record

Altmetrics

Contributors

Author: G. Zioutas
Author: C Chatzinakos
Author: T.-D. Nguyen ORCID iD
Author: L. Pitsoulis

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×