Related papers: Functional analysis via extensions of the band dep…
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…
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…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
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,…
Multi-dimensional functional data arises in numerous modern scientific experimental and observational studies. In this paper we focus on longitudinal functional data, a structured form of multidimensional functional data. Operating within a…
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 recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
This paper examines robust functional data analysis for discretely observed data, where the underlying process encompasses various distributions, such as heavy tail, skewness, or contaminations. We propose a unified robust concept of…
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…
Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are…
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…
A fast nonparametric procedure for classifying functional data is introduced. It consists of a two-step transformation of the original data plus a classifier operating on a low-dimensional hypercube. The functional data are first mapped…
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…
The Oja depth (simplicial volume depth) is one of the classical statistical techniques for measuring the central tendency of data in multivariate space. Despite the widespread emergence of object data like images, texts, matrices or graphs,…
Data depth is a statistical function that generalizes order and quantiles to the multivariate setting and beyond, with applications spanning over descriptive and visual statistics, anomaly detection, testing, etc. The celebrated halfspace…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of 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…
The statistical analysis of functional data is a growing need in many research areas. In particular, a robust methodology is important to study curves, which are the output of experiments in applied statistics. In this paper we study some…
The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…