Related papers: Tail index estimation, concentration and adaptivit…

We propose kernel estimator for the distribution function of unobserved errors in autoregressive time series, based on residuals computed by estimating the autoregressive coefficients with the Yule-Walker method. Under mild assumptions, we…

We consider a regression framework where the design points are deterministic and the errors possibly non-i.i.d. and heavy-tailed (with a moment of order $p$ in $[1,2]$). Given a class of candidate regression functions, we propose a…

There is an increasing interest to understand the dependence structure of a random vector not only in the center of its distribution but also in the tails. Extreme-value theory tackles the problem of modelling the joint tail of a…

In a number of applications, particularly in financial and actuarial mathematics, it is of interest to characterize the tail distribution of a random variable $V$ satisfying the distributional equation $V\stackrel{\mathcal{D}}{=}f(V)$,…

This paper introduces a robust and computationally efficient estimation framework for high-dimensional volatility models in the BEKK-ARCH class. The proposed approach employs data truncation to ensure robustness against heavy-tailed…

We use the fitted Pareto law to construct an accompanying approximation of the excess distribution function. A selection rule of the location of the excess distribution function is proposed based on a stagewise lack-of-fit testing…

We consider the problem of aggregating a general collection of affine estimators for fixed design regression. Relevant examples include some commonly used statistical estimators such as least squares, ridge and robust least squares…

We propose a novel approach for detecting change points in high-dimensional linear regression models. Unlike previous research that relied on strict Gaussian/sub-Gaussian error assumptions and had prior knowledge of change points, we…

Bias reduction in tail estimation has received considerable interest in extreme value analysis. Estimation methods that minimize the bias while keeping the mean squared error (MSE) under control, are especially useful when applying…

Consider a random sample in the max-domain of attraction of a multivariate extreme value distribution such that the dependence structure of the attractor belongs to a parametric model. A new estimator for the unknown parameter is defined as…

We consider non parametric estimation problem for stochastic tomography regression model, i.e. we consider the estimation problem of function of multivariate variables (image) observed through its Radon transformation calculated with the…

In large-scale modern data analysis, first-order optimization methods are usually favored to obtain sparse estimators in high dimensions. This paper performs theoretical analysis of a class of iterative thresholding based estimators defined…

This paper addresses the problem of model selection in the sequence model $Y=\theta+\varepsilon\xi$, when $\xi$ is sub-Gaussian, for non-euclidian loss-functions. In this model, the Penalized Comparison to Overfitting procedure is studied…

We establish new tail estimates for order statistics and for the Euclidean norms of projections of an isotropic log-concave random vector. More generally, we prove tail estimates for the norms of projections of sums of independent…

This paper develops asymptotic approximations of $P(\int_Te^{f(t)}\,dt>b)$ as $b\rightarrow\infty$ for a homogeneous smooth Gaussian random field, $f$, living on a compact $d$-dimensional Jordan measurable set $T$. The integral of an…

In this paper, we propose a reduced-bias estimator of the EVI for Pareto-type tails (heavy-tailed) distributions. This is derived using the weighted least squares method. It is shown that the estimator is unbiased, consistent and…

Motivated by the prominence of Conditional Value-at-Risk (CVaR) as a measure for tail risk in settings affected by uncertainty, we develop a new formula for approximating CVaR based optimization objectives and their gradients from limited…

In this paper non-asymptotic exponential and moment estimates are derived for tail of distribution for discrete time martingale and martingale transform by means of martingale differences in the terms of moments and tails of distributions…

Preferential attachment is widely used to model power-law behavior of degree distributions in both directed and undirected networks. In a directed preferential attachment model, despite the well-known marginal power-law degree…

Quantile regression is an important tool for estimation of conditional quantiles of a response Y given a vector of covariates X. It can be used to measure the effect of covariates not only in the center of a distribution, but also in the…