Improved multivariate normal mean estimation with unknown covariance when p is greater than n Academic Article uri icon


MeSH Major

  • Antibodies, Monoclonal
  • Antineoplastic Agents
  • Protein Kinase Inhibitors
  • Receptor, Epidermal Growth Factor
  • Skin Neoplasms


  • We consider the problem of estimating the mean vector of a p-variate normal (θ,σ) distribution under invariant quadratic loss, (δ-θ)′ σ-1(δ-θ), when the covariance is unknown. We propose a new class of estimators that dominate the usual estimator δ0(X) = X. The proposed estimators of θ depend upon X and an independent Wishart matrix S with n degrees of freedom, however, S is singular almost surely when p >n. The proof of domination involves the development of some new unbiased estimators of risk for the p >n setting. We also find some relationships between the amount of domination and the magnitudes of n and p. © 2012 Institute of Mathematical Statistics.

publication date

  • December 2012



  • Academic Article


Digital Object Identifier (DOI)

  • 10.1214/12-AOS1067

Additional Document Info

start page

  • 3137

end page

  • 3160


  • 40


  • 6