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Point estimators of the Mahalanobis distance in high-dimensional data
Jönköping University, Jönköping International Business School, JIBS, Statistics.
(English)Manuscript (preprint) (Other academic)
Abstract [en]

This paper concerns the problem of estimating the Mahalanobis distance when the dimension of the data matrix is comparable to the sample size. Two different ridge-shrinkage estimators are considered and estimators of related risk functions are derived. The properties of these point estimators are investigated in terms of excess risk and bias relative to the traditional estimator.

Keyword [en]
Ridge estimators, resolvent estimators, inverse covariance matrix, increasing dimension, Mahalanobis distance
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:hj:diva-31980OAI: oai:DiVA.org:hj-31980DiVA: diva2:1037094
Available from: 2016-10-13 Created: 2016-10-13 Last updated: 2016-10-13Bibliographically approved
In thesis
1. Issues of incompleteness, outliers and asymptotics in high dimensional data
Open this publication in new window or tab >>Issues of incompleteness, outliers and asymptotics in high dimensional data
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis consists of four individual essays and an introduction chapter. The essays are in the field of multivariate statistical analysis of High dimensional data. The first essay presents the issue of estimating the inverse covariance matrix alone and when it is used within the Mahalanobis distance in High-dimensional data. Three types of ridge-shrinkage estimators of the inverse covariance matrix are suggested and evaluated through Monte Carlo simulations. The second essay deals with incomplete observations in empirical applications of the Arbitrage Pricing Theory model and the interest is to model the underlying covariance structure among the variables by a few common factors. Two possible solutions to the problem are considered and a

case study using the Swedish OMX data is conducted for demonstration. In the third essay the issue of outlier detection in High-dimensional data is treated. A number of point estimators of the Mahalanobis distance are suggested and their properties are evaluated. In the fourth and last essay the relation between the second central moment of a distribution to its first raw moment is considered in an financial context. Three possible estimators are considered and it is shown that they are consistent even when the dimension increases proportionally to the number of observations.

Place, publisher, year, edition, pages
Jönköping: Jönköping International Business School, 2011. 119 p.
Series
JIBS Dissertation Series, ISSN 1403-0470 ; 069
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-14934 (URN)9789186345181 (ISBN)
Public defence
2011-04-29, B1014, 10:00 (English)
Supervisors
Available from: 2011-05-03 Created: 2011-05-03 Last updated: 2016-10-13Bibliographically approved

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf