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How General is the Vale–Maurelli Simulation Approach?

Published online by Cambridge University Press:  01 January 2025

Njål Foldnes  and
Steffen Grønneberg
Njål Foldnes*
Affiliation:
BI Norwegian Business School
Steffen Grønneberg
Affiliation:
BI Norwegian Business School
*
Correspondence should be made to Njål Foldnes, BI Norwegian Business School, Oslo, Norway. Email: njal.foldnes@bi.no
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Abstract

The Vale–Maurelli (VM) approach to generating non-normal multivariate data involves the use of Fleishman polynomials applied to an underlying Gaussian random vector. This method has been extensively used in Monte Carlo studies during the last three decades to investigate the finite-sample performance of estimators under non-Gaussian conditions. The validity of conclusions drawn from these studies clearly depends on the range of distributions obtainable with the VM method. We deduce the distribution and the copula for a vector generated by a generalized VM transformation, and show that it is fundamentally linked to the underlying Gaussian distribution and copula. In the process we derive the distribution of the Fleishman polynomial in full generality. While data generated with the VM approach appears to be highly non-normal, its truly multivariate properties are close to the Gaussian case. A Monte Carlo study illustrates that generating data with a different copula than that implied by the VM approach severely weakens the performance of normal-theory based ML estimates.

Keywords

Vale–MaurellisimulationMonte Carlomultivariate distributionscopula
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 4 , December 2015 , pp. 1066 - 1083
Copyright
Copyright © 2015 The Psychometric Society

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