Further properties of random orthogonal matrix simulation

Ledermann, Daniel and Alexander, Carol (2012) Further properties of random orthogonal matrix simulation. Mathematics and Computers in Simulation, 83. pp. 56-79. ISSN 0378-4754

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Abstract

Random orthogonal matrix (ROM) simulation is a very fast procedure for generating multivariate random samples that always have exactly the same mean, covariance and Mardia multivariate skewness and kurtosis. This paper investigates how the properties of parametric, data-specific and deterministic ROM simulations are influenced by the choice of orthogonal matrix. Specifically, we consider how cyclic and general permutation matrices alter their time-series properties, and how three classes of rotation matrices – upper Hessenberg, Cayley, and exponential – influence both the unconditional moments of the marginal distributions and the behaviour of skewness when samples are concatenated. We also perform an experiment which demonstrates that parametric ROM simulation can be hundreds of times faster than equivalent Monte Carlo simulation.

Item Type: Article
Keywords: Computational efficiency; L matrix; Quantile; Random orthogonal matrix (ROM); Rotation matrix; Random re-sampling; Simulation
Schools and Departments: School of Business, Management and Economics > Business and Management
Subjects: H Social Sciences > HA Statistics > HA154 Statistical data
H Social Sciences > HA Statistics > HA029 Theory and method of social science statistics
H Social Sciences > HG Finance
Q Science > QA Mathematics > QA0150 Algebra. Including machine theory, game theory
Q Science > QA Mathematics > QA0076 Computer software
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Depositing User: Carol Alexander
Date Deposited: 11 Sep 2012 08:45
Last Modified: 26 Jun 2013 14:36
URI: http://sro.sussex.ac.uk/id/eprint/40633
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