Related papers: Hypergeometric Distribution Revisited: Tail Inequa…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
In this paper, I present a completely new type of upper and lower bounds on the right-tail probabilities of continuous random variables with unbounded support and with semi-bounded support from the left. The presented upper and lower…
We leverage recent advances in heavy-tail approximations for global hypothesis testing with dependent studies to construct approximate confidence regions without modeling or estimating their dependence structures. A non-rejection region is…
In the analysis of survey data it is of interest to estimate and quantify uncertainty about means or totals for each of several non-overlapping subpopulations, or areas. When the sample size for a given area is small, standard confidence…
To segment a sequence of independent random variables at an unknown number of change-points, we introduce new procedures that are based on thresholding the likelihood ratio statistic. We also study confidence regions based on the likelihood…
Using an intrinsic approach, we study some properties of random fields which appear as tail fields of regularly varying stationary random fields. The index set is allowed to be a general locally compact Hausdorff Abelian group $\mathbb{G}$.…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Estimating the structures at high or low quantiles has become an important subject and attracted increasing attention across numerous fields. However, due to data sparsity at tails, it usually is a challenging task to obtain reliable…
The tail of the distribution of a sum of a random number of independent and identically distributed nonnegative random variables depends on the tails of the number of terms and of the terms themselves. This situation is of interest in the…
Insurance data can be asymmetric with heavy tails, causing inadequate adjustments of the usually applied models. To deal with this issue, hierarchical models for collective risk with heavy-tails of the claims distributions that take also…
In this paper non-asymptotic exponential estimates are derived for the tail distribution of polynomial martingale differences in terms unconditional tails distributions of summands. Applications are considered in the theory of polynomials…
Estimation of tail quantities, such as expected shortfall or Value at Risk, is a difficult problem. We show how the theory of nonlinear expectations, in particular the Data-robust expectation introduced in [5], can assist in the…
Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit…
We consider a general regression model, without a scale parameter. Our aim is to construct a confidence interval for a scalar parameter of interest $\theta$ that utilizes the uncertain prior information that a distinct scalar parameter…
There are many ways of measuring and modeling tail-dependence in random vectors: from the general framework of multivariate regular variation and the flexible class of max-stable vectors down to simple and concise summary measures like the…
Sample measures of top centile contributions to the total (concentration) are downward biased, unstable estimators, extremely sensitive to sample size and concave in accounting for large deviations. It makes them particularly unfit in…
It is shown that functions defined on $\{0,1,...,r-1\}^n$ satisfying certain conditions of bounded differences that guarantee sub-Gaussian tail behavior also satisfy a much stronger ``local'' sub-Gaussian property. For self-bounding and…
We review a finite-sampling exponential bound due to Serfling and discuss related exponential bounds for the hypergeometric distribution. We then discuss how such bounds motivate some new results for two-sample empirical processes. Our…
We investigate robust nonparametric regression in the presence of heavy-tailed noise, where the hypothesis class may contain unbounded functions and robustness is ensured via a robust loss function $\ell_\sigma$. Using Huber regression as a…
This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the…