Related papers: General notions of regression depth function
Statistical data depth plays an important role in the analysis of multivariate data sets. The main outcome is a center-outward ordering of the observations that can be used both to highlight features of the underlying distribution of the…
Data depth is a concept in multivariate statistics that measures the centrality of a point in a given data cloud in $\IR^d$. If the depth of a point can be represented as the minimum of the depths with respect to all one-dimensional…
John W. Tukey (1975) defined statistical data depth as a function that determines centrality of an arbitrary point with respect to a data cloud or to a probability measure. During the last decades, this seminal idea of data depth evolved…
A functional data depth provides a center-outward ordering criterion which allows the definition of measures such as median, trimmed means, central regions or ranks in a functional framework. A functional data depth can be global or local.…
In the context of multivariate functional data with individual phase variation, we develop a robust depth-based approach to estimate the main pattern function when cross-component time warping is also present. In particular, we consider the…
The concept of median/consensus has been widely investigated in order to provide a statistical summary of ranking data, i.e. realizations of a random permutation $\Sigma$ of a finite set, $\{1,\; \ldots,\; n\}$ with $n\geq 1$ say. As it…
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…
Statistical depth functions order the elements of a space with respect to their centrality in a probability distribution or dataset. Since many depth functions are maximized in the real line by the median, they provide a natural approach to…
We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…
We propose learning a depth covariance function with applications to geometric vision tasks. Given RGB images as input, the covariance function can be flexibly used to define priors over depth functions, predictive distributions given…
Directional data arise in many applications where observations are naturally represented as unit vectors or as observations on the surface of a unit hypersphere. In this context, statistical depth functions provide a center--outward…
In 1975 John Tukey proposed a multivariate median which is the 'deepest' point in a given data cloud in R^d. Later, in measuring the depth of an arbitrary point z with respect to the data, David Donoho and Miriam Gasko considered…
Statistical analysis of functional data is challenging due to their complex patterns, for which functional depth provides an effective means of reflecting their ordering structure. In this work, we investigate practical aspects of the…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
We investigate nonparametric regression methods based on spatial depth and quantiles when the response and the covariate are both functions. As in classical quantile regression for finite dimensional data, regression techniques developed…
This paper presents a comprehensive review of loss functions and performance metrics in deep learning, highlighting key developments and practical insights across diverse application areas. We begin by outlining fundamental considerations…
For hypothesis testing of functional parameters, given a functional statistic $T_n$ and a functional depth $D$ with respect to the distribution $P_n$ of $T_n$, we propose the depth value $DT_n \equiv D(T_n;P_n)$ as a test statistic, which…
Determining the representativeness of a point within a data cloud has recently become a desirable task in multivariate analysis. The concept of statistical depth function, which reflects centrality of an arbitrary point, appears to be…
Depth is a concept that measures the `centrality' of a point in a given data cloud or in a given probability distribution. Every depth defines a family of so-called trimmed regions. For statistical applications it is desirable that with…
Centrality descriptors are widely used to rank nodes according to specific concept(s) of importance. Despite the large number of centrality measures available nowadays, it is still poorly understood how to identify the node which can be…