| 1. |
- Bodnar, Olha, senior lecturer, 1979-, et al.
(author)
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Robust Surveillance of Covariance Matrices Using a Single Observation
- 2013
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In: Sankhya - The Indian Journal of Statistics. - : Springer. - 0972-7671 .- 0976-3139. ; 76:2, s. 219-256
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Journal article (peer-reviewed)abstract
- In this paper a new technique for monitoring shifts in covariance matrices of Gaussian processes is developed. The processes we monitor are obtained from the covariance matrices estimated using a single observation. These processes follow independent Gaussian distribution in the in-control state, thus allowing for application of standard control charts. Furthermore, in contrary to the existing literature, the suggested procedure is asymptotically robust to the shifts in the mean. The explicit out-of-control distribution for an arbitrary moment of the shift is derived. The performance of numerous multivariate control charts is evaluated in an extensive simulation study and applied to monitoring volatilities on financial markets.
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| 2. |
- Bodnar, Taras, et al.
(author)
-
Distribution of the product of a singular Wishart matrix and a normal vector
- 2014
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In: Theory of Probability and Mathematical Statistics. - : American Mathematical Society (AMS). - 0094-9000 .- 1547-7363. ; :91, s. 1-15
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Journal article (peer-reviewed)abstract
- In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from the product which leads to a considerable improvement in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix.
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| 3. |
- Bodnar, Taras, et al.
(author)
-
Distribution of the product of singular Wishart matrix and normal vector
- 2014
-
In: Theory of Probability and Mathematical Statistics. - 1547-7363. ; :91, s. 1-14
-
Journal article (pop. science, debate, etc.)abstract
- In this paper we derive a very useful formula for the stochastic representation of the product of a singular Wishart matrix with a normal vector. Using this result, the expressions of the density function as well as of the characteristic function are established. Moreover, the derived stochastic representation is used to generate random samples from product which leads to a considerable improvement in the computation efficiency. Finally, we present several important properties of the singular Wishart distribution, like its characteristic function and distributional properties of the partitioned singular Wishart matrix.
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| 4. |
- Bodnar, Taras, et al.
(author)
-
On the exact and approximate distributions of the product of a Wishart matrix with a normal vector
- 2013
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In: Journal of Multivariate Analysis. - : Elsevier. - 0047-259X .- 1095-7243. ; 122, s. 70-81
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Journal article (peer-reviewed)abstract
- In this paper we consider the distribution of the product of a Wishart random matrix and a Gaussian random vector. We derive a stochastic representation for the elements of the product. Using this result, the exact joint density for an arbitrary linear combination of the elements of the product is obtained. Furthermore, the derived stochastic representation allows us to simulate samples of arbitrary size by generating independently distributed chi-squared random variables and standard multivariate normal random vectors for each element of the sample. Additionally to the Monte Carlo approach, we suggest another approximation of the density function, which is based on the Gaussian integral and the third order Taylor expansion. We investigate, with a numerical study, the properties of the suggested approximations. A good performance is documented for both methods.
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