Related papers: Statistics of extremes by oracle estimation
Recently some papers, such as Aban, Meerschaert and Panorska (2006), Nuyts (2010) and Clark (2013), have drawn attention to possible truncation in Pareto tail modelling. Sometimes natural upper bounds exist that truncate the probability…
In this paper we propose a new lifetime model, called the odd generalized exponential linear failure rate distribution. Some statistical properties of the proposed distribution such as the moments, the quantiles, the median, and the mode…
A weighted Gaussian approximation to tail product-limit process for Pareto-like distributions of randomly right-truncated data is provided and a new consistent and asymptotically normal estimator of the extreme value index is derived. A…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
This short communication uses a simple experiment to show that fitting to a power law distribution by using graphical methods based on linear fit on the log-log scale is biased and inaccurate. It shows that using maximum likelihood…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the…
A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the…
We interpret likelihood-based test functions from a geometric perspective where the Kullback-Leibler (KL) divergence is adopted to quantify the distance from a distribution to another. Such a test function can be seen as a sub-Gaussian…
Hyperbolic balance laws with uncertain (random) parameters and inputs are ubiquitous in science and engineering. Quantification of uncertainty in predictions derived from such laws, and reduction of predictive uncertainty via data…
We first describe a general class of optimization problems that describe many natural, economic, and statistical phenomena. After noting the existence of a conserved quantity in a transformed coordinate system, we outline several instances…
A new notion of stochastic ordering is introduced to compare multivariate stochastic risk models with respect to extreme portfolio losses. In the framework of multivariate regular variation comparison criteria are derived in terms of…
The Kullback-Leibler (KL) divergence is frequently used in data science. For discrete distributions on large state spaces, approximations of probability vectors may result in a few small negative entries, rendering the KL divergence…
This paper presents a new model for characterising temporal dependence in exceedances above a threshold. The model is based on the class of trawl processes, which are stationary, infinitely divisible stochastic processes. The model for…
In several applications, ultimately at the largest data, truncation effects can be observed when analysing tail characteristics of statistical distributions. In some cases truncation effects are forecasted through physical models such as…
Empirical risk minimization, a cornerstone in machine learning, is often hindered by the Optimizer's Curse stemming from discrepancies between the empirical and true data-generating distributions.To address this challenge, the robust…
This paper addresses the problem of distributed detection in fixed and switching networks. A network of agents observe partially informative signals about the unknown state of the world. Hence, they collaborate with each other to identify…
Linear regression is a fundamental and popular statistical method. There are various kinds of linear regression, such as mean regression and quantile regression. In this paper, we propose a new one called distribution regression, which…
In the regression setting, given a set of hyper-parameters, a model-estimation procedure constructs a model from training data. The optimal hyper-parameters that minimize generalization error of the model are usually unknown. In practice…
The Kullback-Leibler divergence, the Kullback-Leibler variation, and the Bernstein "norm" are used to quantify discrepancies among probability distributions in likelihood models such as nonparametric maximum likelihood and nonparametric…