On depth measures and dual statistics. A methodology for dealing with general data |
| |
Authors: | Antonio Cuevas Ricardo Fraiman |
| |
Institution: | a Departamento de Matemáticas, Univ. Autónoma de Madrid, Spain b Departamento de Matemática, Univ. de San Andrés, Argentina c Centro de Matemática, Universidad de la República, Uruguay |
| |
Abstract: | A general depth measure, based on the use of one-dimensional linear continuous projections, is proposed. The applicability of this idea in different statistical setups (including inference in functional data analysis, image analysis and classification) is discussed. A special emphasis is made on the possible usefulness of this method in some statistical problems where the data are elements of a Banach space.The asymptotic properties of the empirical approximation of the proposed depth measure are investigated. In particular, its asymptotic distribution is obtained through U-statistics techniques. The practical aspects of these ideas are discussed through a small simulation study and a real-data example. |
| |
Keywords: | primary 62G07 secondary 62G20 |
本文献已被 ScienceDirect 等数据库收录! |
|