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Theory of Probability and Mathematical Statistics

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On the product of a singular Wishart matrix and a singular Gaussian vector in high dimension


Authors: T. Bodnar, S. Mazur, S. Muhinyuza and N. Parolya
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 99 (2018).
Journal: Theor. Probability and Math. Statist. 99 (2019), 39-52
MSC (2010): Primary 60E05, 60E10, 60F05, 62H10, 62E20
DOI: https://doi.org/10.1090/tpms/1078
Published electronically: February 27, 2020
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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we consider the product of a singular Wishart random matrix and a singular normal random vector. A very useful stochastic representation of this product is derived. Using this representation, characteristic function and asymptotic distribution of the product under the double asymptotic regime are established. We further document a good finite sample performance of the obtained high-dimensional asymptotic distribution via an extensive Monte Carlo study.


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Additional Information

T. Bodnar
Affiliation: Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden
Email: taras.bodnar@math.su.se

S. Mazur
Affiliation: Unit of Statistics, School of Business, Örebro University, SE-70182 Örebro, Sweden
Email: stepan.mazur@oru.se

S. Muhinyuza
Affiliation: Department of Mathematics, Stockholm University, Roslagsvägen 101, SE-10691 Stockholm, Sweden; and Department of Mathematics, College of Science and technology, University of Rwanda, P.O. Box 3900, Kigali-Rwanda
Email: stanislas.muhinyuza@math.su.se

N. Parolya
Affiliation: Institute of Statistics, Leibniz University of Hannover, D-30167 Hannover, Germany
Email: parolya@statistik.uni-hannover.de

DOI: https://doi.org/10.1090/tpms/1078
Keywords: Singular Wishart distribution, singular normal distribution, stochastic representation, high-dimensional asymptotics
Received by editor(s): April 28, 2018
Published electronically: February 27, 2020
Additional Notes: The first and third authors appreciate the financial support of SIDA via the project 1683030302.
The second author acknowledges the financial support from the project “Models for macro and financial economics after the financial crisis” (Dnr: P18-0201) funded by the Jan Wallander and Tom Hedelius Foundation.
Article copyright: © Copyright 2020 American Mathematical Society