Related papers: Statistical Depth Functions for Ranking Distributi…
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…
Given additional distributional information in the form of moment restrictions, kernel density and distribution function estimators with implied generalised empirical likelihood probabilities as weights achieve a reduction in variance due…
This paper addresses the problem of rank aggregation, which aims to find a consensus ranking among multiple ranking inputs. Traditional rank aggregation methods are deterministic, and can be categorized into explicit and implicit methods…
We propose a new interpretation of measures of information and disorder by connecting these concepts to group theory in a new way. Entropy and group theory are connected here by their common relation to sets of permutations. A combinatorial…
Consensus is a well-studied problem in distributed sensing, computation and control, yet deriving useful and easily computable bounds on the rate of convergence to consensus remains a challenge. This paper discusses the use of seminorms for…
Rank data arises frequently in marketing, finance, organizational behavior, and psychology. Most analysis of rank data reported in the literature assumes the presence of one or more variables (sometimes latent) based on whose values the…
There has been a flurry of research in recent years on notions of fairness in ranking and recommender systems, particularly on how to evaluate if a recommender allocates exposure equally across groups of relevant items (also known as…
Cone distribution functions from statistics are turned into Multi-Criteria Decision Making tools. It is demonstrated that this procedure can be considered as an upgrade of the weighted sum scalarization insofar as it absorbs a whole…
The classical theory of rank-based inference is entirely based either on ordinary ranks, which do not allow for considering location (intercept) parameters, or on signed ranks, which require an assumption of symmetry. If the median, in the…
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…
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…
Data collection is a fundamental problem in the scenario of big data, where the size of sampling sets plays a very important role, especially in the characterization of data structure. This paper considers the information collection process…
Consider independent observations $(X_1,R_1)$, $(X_2,R_2)$, \ldots, $(X_n,R_n)$ with random or fixed ranks $R_i \in \{1,2,\ldots,k\}$, while conditional on $R_i = r$, the random variable $X_i$ has the same distribution as the $r$-th order…
The concept of statistical depth extends the notions of the median and quantiles to other statistical models. These procedures aim to formalize the idea of identifying deeply embedded fits to a model that are less influenced by…
The need for recognition/approximation of functions in terms of elementary functions/operations emerges in many areas of experimental mathematics, numerical analysis, computer algebra systems, model building, machine learning, approximation…
Persistent homology, while ostensibly measuring changes in topology, captures multiscale geometrical information. It is a natural tool for the analysis of point patterns. In this paper we explore the statistical power of the (persistent…
We examine the relationship between two different types of ranked data, frequencies and magnitudes. We consider data that can be sorted out either way, through numbers of occurrences or size of the measures, as it is the case, say, of moon…
Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on…
Statistical depth functions provide center-outward orderings in spaces of dimension larger than one, where a natural ordering does not exist. The numerical evaluation of such depth functions can be computationally prohibitive, even for…
Representing probability distributions by the gradient of their density functions has proven effective in modeling a wide range of continuous data modalities. However, this representation is not applicable in discrete domains where the…