Related papers: Assessing One-Dimensional Cluster Stability by Ext…
A novel statistical method is proposed and investigated for estimating a heavy tailed density under mild smoothness assumptions. Statistical analyses of heavy-tailed distributions are susceptible to the problem of sparse information in the…
In this paper, we propose a uniformly dithered 1-bit quantization scheme for high-dimensional statistical estimation. The scheme contains truncation, dithering, and quantization as typical steps. As canonical examples, the quantization…
Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…
So-called "classification trimmed likelihood curves" have been proposed as a useful heuristic tool to determine the number of clusters and trimming proportion in trimming-based robust clustering methods. However, these curves needs a…
We offer a survey of recent results on covariance estimation for heavy-tailed distributions. By unifying ideas scattered in the literature, we propose user-friendly methods that facilitate practical implementation. Specifically, we…
Many clustering algorithms when the data are curves or functions have been recently proposed. However, the presence of contamination in the sample of curves can influence the performance of most of them. In this work we propose a robust,…
In high dimensional percolation at parameter $p < p_c$, the one-arm probability $\pi_p(n)$ is known to decay exponentially on scale $(p_c - p)^{-1/2}$. We show the same statement for the ratio $\pi_p(n) / \pi_{p_c}(n)$, establishing a form…
We consider the model introduced by Bilu and Linial (2010), who study problems for which the optimal clustering does not change when distances are perturbed. They show that even when a problem is NP-hard, it is sometimes possible to obtain…
This paper proposes a new test for a change point in the mean of high-dimensional data based on the spatial sign and self-normalization. The test is easy to implement with no tuning parameters, robust to heavy-tailedness and theoretically…
Model selection is a major challenge in non-parametric clustering. There is no universally admitted way to evaluate clustering results for the obvious reason that no ground truth is available. The difficulty to find a universal evaluation…
Robust estimators of location and dispersion are often used in the elliptical model to obtain an uncontaminated and highly representative subsample by trimming the data outside an ellipsoid based in the associated Mahalanobis distance. Here…
We provide a complete taxonomic characterization of robust hierarchical clustering methods for directed networks following an axiomatic approach. We begin by introducing three practical properties associated with the notion of robustness in…
Contamination can severely distort an estimator unless the estimation procedure is suitably robust. This is a well-known issue and has been addressed in Robust Statistics, however, the relation of contamination and distorted variable…
The problem of dimension reduction is of increasing importance in modern data analysis. In this paper, we consider modeling the collection of points in a high dimensional space as a union of low dimensional subspaces. In particular we…
Clustering of data points is a fundamental tool in data analysis. We consider points $X$ in a relaxed metric space, where the triangle inequality holds within a constant factor. The {\em cost} of clustering $X$ by $Q$ is $V(Q)=\sum_{x\in X}…
It has recently been discovered that the conclusions of many highly influential econometrics studies can be overturned by removing a very small fraction of their samples (often less than $0.5\%$). These conclusions are typically based on…
We study the problem of optimal estimation of the density cluster tree under various assumptions on the underlying density. Building up from the seminal work of Chaudhuri et al. [2014], we formulate a new notion of clustering consistency…
Understanding the complex structure of multivariate extremes is a major challenge in various fields from portfolio monitoring and environmental risk management to insurance. In the framework of multivariate Extreme Value Theory, a common…
Nested sampling is an iterative integration procedure that shrinks the prior volume towards higher likelihoods by removing a "live" point at a time. A replacement point is drawn uniformly from the prior above an ever-increasing likelihood…
The trimmed mean of $n$ scalar random variables from a distribution $P$ is the variant of the standard sample mean where the $k$ smallest and $k$ largest values in the sample are discarded for some parameter $k$. In this paper, we look at…