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Issues of incompleteness, outliers and asymptotics in high dimensional data
Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
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: urn:nbn:se:hj:diva-14934ISBN: 9789186345181OAI: oai:DiVA.org:hj-14934DiVA: diva2:414293
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
List of papers
1. An Investigation and Development of Three Estimators of Inverse Covariance Matrices With Applications to the Mahalanobis Distance
Open this publication in new window or tab >>An Investigation and Development of Three Estimators of Inverse Covariance Matrices With Applications to the Mahalanobis Distance
2010 (English)Report (Other academic)
27 p.
Series
JIBS Working Papers, 2010-11
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-14515 (URN)
Available from: 2011-02-01 Created: 2011-02-01 Last updated: 2016-10-13Bibliographically approved
2. The Incompleteness Problem of the APT model.
Open this publication in new window or tab >>The Incompleteness Problem of the APT model.
2011 (English)In: Computational Economics, ISSN 0927-7099, E-ISSN 1572-9974, Vol. 38, no 2, 129-151 p.Article in journal (Refereed) Published
Abstract [en]

The Arbitrage Pricing Theory provides a theory to quantify risk and the reward for taking it. While the theory itself is sound from most perspectives, its empirical version is connected with several shortcomings. One extremely delicate problem arises because the set of observable asset returns rarely has a history of complete observations. Traditionally, this problem has been solved by simply excluding assets without a complete set of observations from the analysis. Unfortunately, such a methodology may be shown to (i) lead for any fixed time period to selection bias in that only the largest companies will remain and (ii) lead to an asymptotically empty set containing no observations at all. This paper discusses some possible solutions to this problem and also provides a case study containing Swedish OMX data for demonstration.

National Category
Economics
Identifiers
urn:nbn:se:hj:diva-15767 (URN)10.1007/s10614-011-9255-1 (DOI)
Available from: 2011-08-12 Created: 2011-08-12 Last updated: 2016-10-13Bibliographically approved
3. Point estimators of the Mahalanobis distance in high-dimensional data
Open this publication in new window or tab >>Point estimators of the Mahalanobis distance in high-dimensional data
(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
Ridge estimators, resolvent estimators, inverse covariance matrix, increasing dimension, Mahalanobis distance
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-31980 (URN)
Available from: 2016-10-13 Created: 2016-10-13 Last updated: 2016-10-13Bibliographically approved
4. Estimating mean-standard deviation ratios of financial data
Open this publication in new window or tab >>Estimating mean-standard deviation ratios of financial data
2012 (English)In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 39, no 3, 657-671 p.Article in journal (Refereed) Published
Abstract [en]

This article treats the problem of linking the relation between excess return and risk of financial assets when the returns follow a factor structure. The authors propose three different estimators and their consistencies are established in cases when the number of assets in the cross-section (n) and the number of observations over time (T) are of comparable size. An empirical investigation is conducted on the Stockholm stock exchange market where the mean-standard deviation ratio is calculated for small- mid- and large cap segments, respectively.

Keyword
return-risk ratio, increasing dimension asymptotics, coefficient of variation, Arbitrage Pricing Theory model
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:hj:diva-15730 (URN)10.1080/02664763.2011.610443 (DOI)
Available from: 2011-08-01 Created: 2011-08-01 Last updated: 2016-10-13Bibliographically approved

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