30:56
publiée le 14 janvier 2025
From robust tests to robust Bayes-like posterior distribution
De Yannick Baraud
Shrinkage estimation of mean for complex multivariate normal distribution with unknown covariance when p > n
Apparaît dans la collection : Mathematical Methods of Modern Statistics 2 / Méthodes mathématiques en statistiques modernes 2
We consider the problem of estimating the mean vector of the multivariate complex normaldistribution with unknown covariance matrix under an invariant loss function when the samplesize is smaller than the dimension of the mean vector. Following the approach of Chételat and Wells (2012, Ann.Statist, p. 3137–3160), we show that a modification of Baranchik-tpye estimatorsbeats the MLE if it satisfies certain conditions. Based on this result, we propose the James-Stein-like shrinkage and its positive-part estimators.
