A topologically valid definition of depth for functional data
From MaRDI portal
Publication:1790314
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
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