We propose a class of robust estimates for multivariate linear models. Based
on the approach of MM estimation (Yohai 1987), we estimate the regression
coefficients and the covariance matrix of the errors simultaneously. These
estimates have both high breakdown point and high asymptotic efficiency under
Gaussian errors. We prove consistency and asymptotic normality assuming errors
with an elliptical distribution. We describe an iterative algorithm for the
numerical calculation of these estimates. The advantages of the proposed
estimates over their competitors are demonstrated through both simulated and
real data.Comment: 8 figures and 5 table
A density function is generally not well defined in functional data context, but we can define a surrogate of a probability density, also called pseudo-density, when the small ball probability can be approximated by the product of two independent functions, one depending only on the centre of the ball. The aim of this paper is to study two kernel methods for estimating a surrogate probability density for functional data. We present asymptotic properties of these estimators: the convergence in probability and their rates. Simulations are given, including a functional version of smoother bootstrap selection of the parameters of the estimate.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.