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How General is the Vale-Maurelli Simulation Approach?

Njål Foldnes1, Steffen Grønneberg2

  • 1BI Norwegian Business School, Oslo, Norway. njal.foldnes@bi.no.

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|August 7, 2014
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Summary

The Vale-Maurelli (VM) method generates non-normal data but retains Gaussian properties. Using a different copula than implied by VM weakens normal-theory ML estimates in Monte Carlo studies.

Keywords:
Monte CarloVale–Maurellicopulamultivariate distributionssimulation

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Area of Science:

  • Statistics
  • Probability Theory
  • Computational Statistics

Background:

  • The Vale-Maurelli (VM) approach is widely used for generating non-normal multivariate data in Monte Carlo simulations.
  • Its application relies on Fleishman polynomials applied to Gaussian random vectors.
  • The validity of simulation results depends on the range of distributions achievable with the VM method.

Purpose of the Study:

  • To deduce the distribution and copula of vectors generated by a generalized VM transformation.
  • To analyze the relationship between VM-generated data and underlying Gaussian distributions.
  • To investigate the impact of using different copulas in Monte Carlo studies.

Main Methods:

  • Derivation of the general distribution for Fleishman polynomials.
  • Deduction of the multivariate distribution and copula for generalized VM transformations.
  • Conducting a Monte Carlo study to assess the performance of ML estimates.

Main Results:

  • The distribution of VM-generated data is fundamentally linked to the underlying Gaussian distribution and copula.
  • Despite appearing non-normal, VM-generated data exhibits multivariate properties close to the Gaussian case.
  • Generating data with a non-implied copula significantly degrades the performance of normal-theory ML estimates.

Conclusions:

  • The Vale-Maurelli method's multivariate properties are intrinsically tied to Gaussian distributions.
  • Researchers must be cautious about copula selection in simulations using the VM approach.
  • Deviations from the VM-implied copula can lead to unreliable statistical inference.