On the fractional moments of a truncated centered multivariate normal distribution

In this paper, we study the fractional moments of a truncated centered multivariate normal distribution, with a focus on their computation. We develop computational methods, including ones based on the holonomic gradient method, the second-order Laplace approximation, and the Monte Carlo method. The...

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Published inCommunications in statistics. Simulation and computation Vol. 51; no. 7; pp. 3923 - 3942
Main Authors Ogawa, Mitsunori, Nakamoto, Kazuki, Sei, Tomonari
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 03.07.2022
Taylor & Francis Ltd
Subjects
Algebraic statistics
Approximation
Holonomic gradient method
Laplace approximation
Monte Carlo method
Monte Carlo simulation
Multivariate analysis
Normal distribution
Robustness (mathematics)
Statistical analysis
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Abstract In this paper, we study the fractional moments of a truncated centered multivariate normal distribution, with a focus on their computation. We develop computational methods, including ones based on the holonomic gradient method, the second-order Laplace approximation, and the Monte Carlo method. These methods enable us to compute higher order fractional moments without evaluating multiple integrals. Via numerical experiments, we investigate their performances. Some applications, including robust graphical modeling based on the alternative multivariate t-distribution, are also presented.
AbstractList In this paper, we study the fractional moments of a truncated centered multivariate normal distribution, with a focus on their computation. We develop computational methods, including ones based on the holonomic gradient method, the second-order Laplace approximation, and the Monte Carlo method. These methods enable us to compute higher order fractional moments without evaluating multiple integrals. Via numerical experiments, we investigate their performances. Some applications, including robust graphical modeling based on the alternative multivariate t-distribution, are also presented.
Author Sei, Tomonari
Ogawa, Mitsunori
Nakamoto, Kazuki
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SubjectTerms Algebraic statistics
Approximation
Holonomic gradient method
Laplace approximation
Monte Carlo method
Monte Carlo simulation
Multivariate analysis
Normal distribution
Robustness (mathematics)
Statistical analysis
Title On the fractional moments of a truncated centered multivariate normal distribution
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