1. Weak convergence of discretely observed functional data with applications
- Author
-
Irène Gijbels, Stanislav Nagy, and Daniel Hlubinka
- Subjects
Statistics and Probability ,Numerical Analysis ,Mathematical optimization ,Weak convergence ,05 social sciences ,Mean value ,Empirical measure ,01 natural sciences ,010104 statistics & probability ,Consistency (statistics) ,0502 economics and business ,Applied mathematics ,0101 mathematics ,Statistics, Probability and Uncertainty ,050205 econometrics ,Mathematics ,Counterexample - Abstract
© 2015 Elsevier Inc. A general result on weak convergence of the empirical measure of discretely observed functional data is shown. It is applied to the problem of estimation of functional mean value, and the problem of consistency of various types of depth for functional data. Counterexamples illustrating the fact that the assumptions as stated cannot be dropped easily are given. publisher: Elsevier articletitle: Weak convergence of discretely observed functional data with applications journaltitle: Journal of Multivariate Analysis articlelink: http://dx.doi.org/10.1016/j.jmva.2015.06.006 content_type: article copyright: Copyright © 2015 Elsevier Inc. All rights reserved. ispartof: Journal of Multivariate Analysis vol:146 pages:46-62 status: published
- Published
- 2016