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Robust multivariate estimation based on statistical depth filters
- Source :
- TEST. 30:935-959
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- In the classical contamination models, such as the gross-error (Huber and Tukey contamination model or Case-wise Contamination), observations are considered as the units to be identified as outliers or not. This model is very useful when the number of considered variables is moderately small. Alqallaf et al. [2009] shows the limits of this approach for a larger number of variables and introduced the Independent contamination model (Cell-wise Contamination) where now the cells are the units to be identified as outliers or not. One approach to deal, at the same time, with both type of contamination is filter out the contaminated cells from the data set and then apply a robust procedure able to handle case-wise outliers and missing values. Here we develop a general framework to build filters in any dimension based on statistical data depth functions. We show that previous approaches, e.g. Agostinelli et al. [2015a] and Leung et al. [2017], are special cases. We illustrate our method by using the half-space depth.<br />Comment: 25 pages, 11 figures. TEST (2021)
- Subjects :
- Statistics and Probability
Multivariate statistics
Mathematics - Statistics Theory
Statistics Theory (math.ST)
62G35 62G05
01 natural sciences
010104 statistics & probability
Case-wise contamination
Dimension (vector space)
0502 economics and business
Statistics
FOS: Mathematics
0101 mathematics
Statistical depth functions
050205 econometrics
Mathematics
05 social sciences
Robust statistics
Filters
Filter (signal processing)
Contamination
Missing data
Cell-wise contamination
Data set
Outlier
Depth filter
Statistics, Probability and Uncertainty
Subjects
Details
- ISSN :
- 18638260 and 11330686
- Volume :
- 30
- Database :
- OpenAIRE
- Journal :
- TEST
- Accession number :
- edsair.doi.dedup.....56422952f586cd151736842861348894