Related papers: Robust and efficient estimation for the Generalize…
Accurately estimating high quantiles beyond the largest observed value is crucial for risk assessment and devising effective adaptation strategies to prevent a greater disaster. The generalized extreme value distribution is widely used for…
Randomness in scientific estimation is generally assumed to arise from unmeasured or uncontrolled factors. However, when combining subjective probability estimates, heterogeneity stemming from people's cognitive or information diversity is…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
In testing of hypothesis the robustness of the tests is an important concern. Generally, the maximum likelihood based tests are most efficient under standard regularity conditions, but they are highly non-robust even under small deviations…
In the current paper, the estimation of the probability density function and the cumulative distribution function of the Topp-Leone distribution is considered. We derive the following estimators: maximum likelihood estimator, uniformly…
Extreme value statistics provides accurate estimates for the small occurrence probabilities of rare events. While theory and statistical tools for univariate extremes are well-developed, methods for high-dimensional and complex data sets…
Parameter estimation is one of the most important tasks in statistics, and is key to helping people understand the distribution behind a sample of observations. Traditionally parameter estimation is done either by closed-form solutions…
We are interested in the problem of robust parametric estimation of a density from $n$ i.i.d. observations. By using a practice-oriented procedure based on robust tests, we build an estimator for which we establish non-asymptotic risk…
Over the last decades, the family of $\alpha$-stale distributions has proven to be useful for modelling in telecommunication systems. Particularly, in the case of radar applications, finding a fast and accurate estimation for the amplitude…
We construct and analyze an estimator of association between random variables based on their similarity in both direction and magnitude. Under special conditions, the proposed measure becomes a robust and consistent estimator of the linear…
Extreme events are the major weather-related hazard for humanity. It is then of crucial importance to have a good understanding of their statistics and to be able to forecast them. However, lack of sufficient data makes their study…
The regular variation model for multivariate extremes decomposes the joint distribution of the extremes in polar coordinates in terms of the angles and the norm of the random vector as the product of two independent densities: the angular…
This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
The Dirichlet distribution, also known as multivariate beta, is the most used to analyse frequencies or proportions data. Maximum likelihood is widespread for estimation of Dirichlet's parameters. However, for small sample sizes, the…
We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…
In this study, we propose a robust mixture regression procedure based on the skew t distribution to model heavy-tailed and/or skewed errors in a mixture regression setting. Using the scale mixture representation of the skew t distribution,…
In multivariate extreme value analysis, the nature of the extremal dependence between variables should be considered when selecting appropriate statistical models. Interest often lies with determining which subsets of variables can take…
We present a novel statistical treatment, the "metastatistics of extreme events", for calculating the frequency of extreme events. This approach, which is of general validity, is the proper statistical framework to address the problem of…
We propose a method for the accurate estimation of rare event or failure probabilities for expensive-to-evaluate numerical models in high dimensions. The proposed approach combines ideas from large deviation theory and adaptive importance…