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Stein’s method for the Wishart distribution

Author

Listed:
  • Bailly, Gabriel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Gaunt, Robert E.
  • Ouimet, Frédéric

  • Richards, Donald
  • von Sachs, Rainer

Abstract

In this work, we develop Stein’s method for the Wishart distribution on the cone of positive definite matrices. We establish the basic ingredients of a Wishart Stein framework: we derive an extended-generator-based Stein characterization from the Wishart diffusion process, identify the corresponding transition semigroup through the noncentral Wishart law, provide an explicit semigroup representation for the solution of the Stein equation, and obtain regularity estimates for the solution. The new methodology is demonstrated in four applications: (i) an order n−1 bound, for smooth test functions, for the Wishart approximation of uncentered group-mean scatter matrices in MANOVA; (ii) a quantitative multivariate Satterthwaite approximation; (iii) local/integrated De Bruijn identities and logarithmic Sobolev inequalities for the Wishart mea- sure; and (iv) Stein’s method of moments for the shape and scale parameters, including structured scale estimation.

Suggested Citation

  • Bailly, Gabriel & Gaunt, Robert E. & Ouimet, Frédéric & Richards, Donald & von Sachs, Rainer, 2026. "Stein’s method for the Wishart distribution," LIDAM Discussion Papers ISBA 2026021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvad:2026021
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