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How to simulate normal data sets with the desired correlation structure
Authors:Francisco Arteaga  Alberto Ferrer
Affiliation:a Catholic University of Valencia San Vicente Mártir, Valencia, Spain
b Universidad Politécnica de Valencia, Valencia, Spain
Abstract:The Cholesky decomposition is a widely used method to draw samples from multivariate normal distribution with non-singular covariance matrices. In this work we introduce a simple method by using singular value decomposition (SVD) to simulate multivariate normal data even if the covariance matrix is singular, which is often the case in chemometric problems. The covariance matrix can be specified by the user or can be generated by specifying a subset of the eigenvalues. The latter can be an advantage for simulating data sets with a particular latent structure. This can be useful for testing the performance of chemometric methods with data sets matching the theoretical conditions for their applicability; checking their robustness when the hypothesized properties fail; or generating data from multi-stage or multi-phase processes.
Keywords:Simulation  Multivariate normal  Singular value decomposition  Eigenvalues
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