Related papers: Mean estimation and regression under heavy-tailed …
Constant-specified and exponential concentration inequalities play an essential role in the finite-sample theory of machine learning and high-dimensional statistics area. We obtain sharper and constants-specified concentration inequalities…
The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…
The paper proposes some robust estimators of the finite population mean. Such estimators are particularly suitable in the presence of some outlying observations. Included as special cases of our general result are robust versions of the…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
We obtain an uniform tail estimates for natural normed sums of independent random variables (r.v.) with regular varying tails of distributions. We give also many examples on order to show the exactness of offered estimates and discuss some…
Datasets with extreme observations and/or heavy-tailed error distributions are commonly encountered and should be analyzed with careful consideration of these features from a statistical perspective. Small deviations from an assumed model,…
We develop an unsupervised mixture model for non-negative, skewed and heavy-tailed data, such as losses in actuarial and risk management applications. The mixture has a lognormal component, which is usually appropriate for the body of the…
We investigate the high-dimensional properties of robust regression estimators in the presence of heavy-tailed contamination of both the covariates and response functions. In particular, we provide a sharp asymptotic characterisation of…
The multivariate version of the Mixed Tempered Stable is proposed. It is a generalization of the Normal Variance Mean Mixtures. Characteristics of this new distribution and its capacity in fitting tails and capturing dependence structure…
We analyze the complexity of sampling from a class of heavy-tailed distributions by discretizing a natural class of It\^o diffusions associated with weighted Poincar\'e inequalities. Based on a mean-square analysis, we establish the…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
Heavy-tailed models are used as a way to gain robustness against outliers in Bayesian analyses. In frequentist analyses, M-estimators are often employed. In this paper, the two approaches are tentatively reconciled by considering…
We consider regularly varying random vectors. Our goal is to estimate in a non-parametric way some characteristics related to conditioning on an extreme event, like the tail dependence coefficient. We introduce a quasi-spectral…
We consider the problem of estimating the mean of a random vector based on i.i.d. observations and adversarial contamination. We introduce a multivariate extension of the trimmed-mean estimator and show its optimal performance under minimal…
Rank regression offers robustness to outliers and heavy-tailed response distributions, invariance to monotonic transformations, and improved efficiency under non-Gaussian errors, making it a versatile tool for analyzing complex data. This…
Recently, the concept of tail dependence has been discussed in financial applications related to market or credit risk. The multivariate extreme value theory is a proper tool to measure and model dependence, for example, of large loss…
Distributed data naturally arise in scenarios involving multiple sources of observations, each stored at a different location. Directly pooling all the data together is often prohibited due to limited bandwidth and storage, or due to…
This paper investigates the large sample properties of local regression distribution estimators, which include a class of boundary adaptive density estimators as a prime example. First, we establish a pointwise Gaussian large sample…
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…
Including prior information about model parameters is a fundamental step of any Bayesian statistical analysis. It is viewed positively by some as it allows, among others, to quantitatively incorporate expert opinion about model parameters.…