Related papers: Depth statistics
Despite the renewed interest in the Newey and Powell (1987) concept of expectiles in fields such as econometrics, risk management, and extreme value theory, expectile regression---or, more generally, M-quantile regression---unfortunately…
The regression depth of a hyperplane with respect to a set of n points in R^d is the minimum number of points the hyperplane must pass through in a rotation to vertical. We generalize hyperplane regression depth to k-flats for any k between…
We establish a definition of ordinal patterns for multivariate data sets based on the concept of Tukey's halfspace depth. Given the definition of these \emph{depth patterns}, we are interested in the probabilities of observing specific…
A new multivariate concept of quantile, based on a directional version of Koenker and Bassett's traditional regression quantiles, is introduced for multivariate location and multiple-output regression problems. In their empirical version,…
Notion of median in one dimension is a foundational element in nonparametric statistics. It has been extended to multi-dimensional cases both in location and in regression via notions of data depth. Regression depth (RD) and projection…
Diversity can be broadly defined as the presence of meaningful variation across elements, which can be viewed from multiple perspectives, including statistical variation and geometric structural richness in the dataset. Existing diversity…
Directional data are constrained to lie on the unit sphere of~$\mathbb{R}^q$ for some~$q\geq 2$. To address the lack of a natural ordering for such data, depth functions have been defined on spheres. However, the depths available either…
The scatter halfspace depth (sHD) is an extension of the location halfspace (also called Tukey) depth that is applicable in the nonparametric analysis of scatter. Using sHD, it is possible to define minimax optimal robust scatter estimators…
Topological data analysis (TDA) provides insight into data shape. The summaries obtained by these methods are principled global descriptions of multi-dimensional data whilst exhibiting stable properties such as robustness to deformation and…
The Maximum Depth was the first attempt to use data depths instead of multivariate raw data to construct a classification rule. Recently, the DD-classifier has solved several serious limitations of the Maximum Depth classifier but some…
Anomaly detection is a branch of data analysis and machine learning which aims at identifying observations that exhibit abnormal behaviour. Be it measurement errors, disease development, severe weather, production quality default(s) (items)…
Depth notions in regression have been systematically proposed and examined in Zuo (2018). One of the prominent advantages of notion of depth is that it can be directly utilized to introduce median-type deepest estimating functionals (or…
Statistical depth functions are a standard tool in nonparametric statistics to extend order-based univariate methods to the multivariate setting. Since there is no universally accepted total order for fuzzy data (even in the univariate…
Topological Data Analysis (TDA) provides a toolkit for the study of the shape of high dimensional and complex data. While operating on a space of persistence diagrams is cumbersome, persistence norms provide a simple real value measure of…
This paper introduces several depths for random sets with possibly non-convex realisations, proposes ways to estimate the depths based on the samples and compares them with existing ones. The depths are further applied for the comparison…
In this paper, we investigate the differentially private estimation of data depth functions and their associated medians. We introduce several methods for privatizing depth values at a fixed point, and show that for some depth functions,…
Notions of depth in regression have been introduced and studied in the literature. The most famous example is Regression Depth (RD), which is a direct extension of location depth to regression. The projection regression depth (PRD) is the…
Confidence intervals are a popular way to visualize and analyze data distributions. Unlike p-values, they can convey information both about statistical significance as well as effect size. However, very little work exists on applying…
There has been extensive work on data depth-based methods for robust multivariate data analysis. Recent developments have moved to infinite-dimensional objects such as functional data. In this work, we propose a new notion of depth, the…
In many problems from multivariate analysis, the parameter of interest is a shape matrix, that is, a normalized version of the corresponding scatter or dispersion matrix. In this paper, we propose a depth concept for shape matrices that…