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A simple simulation technique for nonnormal data with prespecified skewness, kurtosis, and covariance matrix

Foldnes, Njål; Olsson, Ulf Henning
Journal article, Peer reviewed
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URI
http://hdl.handle.net/11250/2404335
Date
2016
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  • Scientific articles [1334]
Original version
Multivariate Behavioral Research, 51(2016)2-3: 207-219   http://dx.doi.org/10.1080/00273171.2015.1133274
Abstract
We present and investigate a simple way to generate non-normal data using linear combinations of independent generator (IG) variables. The simulated data have prespecified univariate skewness and kurtosis, and a given covariance matrix. In contrast to the widely used Vale-Maurelli (VM) transform, the obtained data is shown to have a non-Gaussian copula. Analytically, we obtain asymptotic robustness conditions for the IG distribution. Empirically, we show that popular test statistics in covariance analysis tend to reject true models more often under the IG transform than under the VM transform. This implies that overly optimistic evaluations of stimators and fit statistics in covariance sstructure analysis may be tempered by including the IG transform for non-normal data generation. We provide an implementation of the IG transform in the R environment.
Description
This is the accepted, refereed and final manuscript to the article published
Publisher
Taylor & Francis
Journal
Multivariate Behavioral Research

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