A topologically valid definition of depth for functional data

DOI10.1214/15-STS532zbMath1436.62720arXiv1410.5686OpenAlexW2964259247MaRDI QIDQ1790314

Heather Battey, Alicia Nieto-Reyes

Publication date: 2 October 2018

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1410.5686

zbMATH Keywords

robustnessmultivariate statisticspartial observabilityfunctional datastatistical depth

Mathematics Subject Classification ID

Estimation in multivariate analysis (62H12) Functional data analysis (62R10) Nonparametric robustness (62G35) Topological data analysis (62R40)

Related Items (23)

An integrated local depth measure ⋮ Choosing among notions of multivariate depth statistics ⋮ A notion of depth for sparse functional data ⋮ A unified framework on defining depth for point process using function smoothing ⋮ Functional outlier detection and taxonomy by sequential transformations ⋮ Statistical depth in abstract metric spaces ⋮ On a general definition of depth for functional data ⋮ Integrated Depths for Partially Observed Functional Data ⋮ Nonparametric depth and quantile regression for functional data ⋮ Halfspace depths for scatter, concentration and shape matrices ⋮ Halfspace depth and floating body ⋮ Fusing data depth with complex networks: community detection with prior information ⋮ Detecting a structural change in functional time series using local Wilcoxon statistic ⋮ Depth-based classification for relational data with multiple attributes ⋮ A topologically valid construction of depth for functional data ⋮ Directional outlyingness for multivariate functional data ⋮ On general notions of depth for regression ⋮ Depth for curve data and applications ⋮ Dirichlet depths for point process ⋮ Pareto depth for functional data ⋮ Quantifying the closeness to a set of random curves via the mean marginal likelihood ⋮ On projection methods for functional time series forecasting ⋮ Detecting and classifying outliers in big functional data

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Nonlinear manifold representations for functional data
• Some intriguing properties of Tukey's half-space depth
• On data depth in infinite dimensional spaces
• A half-region depth for functional data
• Integrated data depth for smooth functions and its application in supervised classification
• On a notion of data depth based on random simplices
• Robust estimation and classification for functional data via projection-based depth notions
• On depth measures and dual statistics. A methodology for dealing with general data
• The random Tukey depth
• Multivariate analysis by data depth: Descriptive statistics, graphics and inference. (With discussions and rejoinder)
• General notions of statistical depth function.
• Trimmed means for functional data
• Weak convergence and empirical processes. With applications to statistics
• Smoothed functional principal components analysis by choice of norm
• On the performance of some robust nonparametric location measures relative to a general notion of multivariate symmetry
• Nonparametrically consistent depth-based classifiers
• The spatial distribution in infinite dimensional spaces and related quantiles and depths
• From Depth to Local Depth: A Focus on Centrality
• On a Geometric Notion of Quantiles for Multivariate Data
• Lectures on Stochastic Programming
• The multivariate L ₁ -median and associated data depth
• Real Analysis and Probability
• DD-Classifier: Nonparametric Classification Procedure Based onDD-Plot
• Multivariate Functional Halfspace Depth
• On the Concept of Depth for Functional Data
• A General Qualitative Definition of Robustness
• The 1972 Wald Lecture Robust Statistics: A Review
• A Tilting Approach to Ranking Influence
• Linear Manifold Modelling of Multivariate Functional Data
• Mathematical Analysis of Random Noise
• The depth function of a population distribution.

This page was built for publication: A topologically valid definition of depth for functional data