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Stein-Haff Identity for the Exponential Family
Stockholm University, Faculty of Science, Department of Mathematics.ORCID iD: 0000-0003-3403-6805
2018 (English)In: Theory of Probability and Mathematical Statistics, ISSN 0094-9000, Vol. 99Article in journal (Refereed) Accepted
Abstract [en]

In this paper, the Stein-Haff identity is established for positive-definite and symmetric random matrices belonging to the exponential family. The identity is then applied to the matrix-variate gamma distribution, and an estimator that dominates the maximum likelihood estimator in terms of Stein's loss is obtained. Finally, a simulation study is conducted in order to support the theoretical results.

Place, publisher, year, edition, pages
2018. Vol. 99
Keywords [en]
Random matrices, matrix-variate gamma distribution, decision theory
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:su:diva-164942OAI: oai:DiVA.org:su-164942DiVA, id: diva2:1280862
Available from: 2019-01-21 Created: 2019-01-21 Last updated: 2019-03-25Bibliographically approved
In thesis
1. Modeling Realized Covariance of Asset Returns
Open this publication in new window or tab >>Modeling Realized Covariance of Asset Returns
2019 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In this thesis, which consists of two papers, we consider the modeling of positive definitive symmetric matrices, in particular covariance matrices of financial asset returns. The return covariance matrix describes the magnitude in which prices of financial assets tend to change over time, and how price changes between different assets are related. It is an instrumental quantity in many financial applications, and furthermore, an important component in understanding the dynamics present prior to and during times of financial turbulence, such as the 2008 financial crisis.

In the first paper, we provide several goodness-of-fit tests applicable to models driven by a centralized Wishart process. To apply such a distributional assumption has become a popular way of modeling the stochastic properties of time-series of realized covariance matrices for asset returns. The paper includes a simulation study that aims to investigate how the tests perform under model uncertainty stemming from parameter estimation. In addition, the presented methods are used to evaluate the fit of a typical model of realized covariance adapted to real data on six stocks traded on the New York Stock Exchange.

The second paper considers positive definite and symmetric random matrices of the exponential family. Under certain conditions for this class of distributions, we derive the Stein-Haff identity. Furthermore, we determine this identity in the case of the matrix-variate gamma distribution and apply it in order to present an estimator that outperforms the maximum likelihood estimator in terms of Stein's loss function. Finally, a small simulation study is conducted to support the theoretical results.

Place, publisher, year, edition, pages
Stockholm, Sweden: Stockholm University, 2019. p. 74
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
urn:nbn:se:su:diva-167297 (URN)
Presentation
2019-04-11, Room 22, Kräftriket 5A, 114 19 Stockholm, 10:00 (English)
Opponent
Supervisors
Available from: 2019-03-27 Created: 2019-03-25 Last updated: 2019-03-27Bibliographically approved

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