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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 m and scatter matrix S of an elliptically symmetric t distribution on
Externí odkaz:
http://arxiv.org/abs/0801.3052
For positive integers d, r, and M, we consider the class of rational functions on real d-dimensional space whose denominators are products of at most r functions of the form 1+Q(x) where each Q is a quadratic form with eigenvalues bounded above by M
Externí odkaz:
http://arxiv.org/abs/0709.2449
Autor:
Dudley, R. M.
Publikováno v:
IMS Lecture Notes Monograph Series 2006, Vol. 51, 207-219
Assumptions on a likelihood function, including a local Glivenko-Cantelli condition, imply the existence of M-estimators converging to an M-functional. Scatter matrix-valued estimators, defined on all empirical measures on ${\Bbb{R}}^d$ for $d\geq 2$
Externí odkaz:
http://arxiv.org/abs/math/0612709