Differentiability of t-functionals of location and scatter
R. M. Dudley, Sergiy Sidenko, Zuoqin Wang · The Annals of Statistics · 2009
The paper aims at finding widely and smoothly defined nonparametric location and scatter functionals. As a convenient vehicle, maximum likelihood estimation of the location vector μ and scatter matrix Σ of an elliptically symmetric t distribution on ℝd with degrees of freedom ν>1 extends to an M-functional defined on all probability distributions P in a weakly open, weakly dense domain U. Here U consists of P putting not too much mass in hyperplanes of dimension