منابع مشابه
On the Breakdown Properties of Some Multivariate M-Functionals
For probability distributions on IR, a detailed study of the breakdown properties of some multivariate M-functionals related to Tyler’s (1987a) “distribution-free” M-functional of scatter is given. These include a symmetrized version of Tyler’s M-functional of scatter, and the multivariate t M-functionals of location and scatter. It is shown that for “smooth” distributions, the (contamination) ...
متن کاملDifferentiability of M-functionals of Location and Scatter Based on T Likelihoods
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 R 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 . Her...
متن کاملDifferentiability of t-functionals of location and scatter
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 R 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 . Her...
متن کاملSome facts about functionals of location and scatter
Assumptions on a likelihood function, including a local GlivenkoCantelli condition, imply the existence of M-estimators converging to an Mfunctional. Scatter matrix-valued estimators, defined on all empirical measures on R for d ≥ 2, and equivariant under all, including singular, affine transformations, are shown to be constants times the sample covariance matrix. So, if weakly continuous, they...
متن کاملTractability of Approximating Multivariate Linear Functionals
We review selected tractability results for approximating linear tensor product functionals defined over reproducing kernel Hilbert spaces. This review is based on Volume II of our book [5] Tractability of Multivariate Problems. In particular, we show that all non-trivial linear tensor product functionals defined over a standard tensor product unweighted Sobolev space suffer the curse of dimens...
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ژورنال
عنوان ژورنال: Statistics Surveys
سال: 2015
ISSN: 1935-7516
DOI: 10.1214/15-ss109