Related papers: Estimation of conditional laws given an extreme co…
U-statistics constitute a large class of estimators, generalizing the empirical mean of a random variable $X$ to sums over every $k$-tuple of distinct observations of $X$. They may be used to estimate a regular functional $\theta(P_{X})$ of…
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…
Simultaneous concurrence of extreme values across multiple climate variables can result in large societal and environmental impacts. Therefore, there is growing interest in understanding these concurrent extremes. In many applications, not…
There are several estimators of conditional probability from observed frequencies of features. In this paper, we propose using the lower limit of confidence interval on posterior distribution determined by the observed frequencies to…
In risk management, often the probability must be estimated that a random vector falls into an extreme failure set. In the framework of bivariate extreme value theory, we construct an estimator for such failure probabilities and analyze its…
Consider a high-dimensional linear regression problem, where the number of covariates is larger than the number of observations and the interest is in estimating the conditional variance of the response variable given the covariates. A…
Multivariate normal mixtures provide a flexible model for high-dimensional data. They are widely used in statistical genetics, statistical finance, and other disciplines. Due to the unboundedness of the likelihood function, classical…
Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional…
In this paper, we use quantization to construct a nonparametric estimator of conditional quantiles of a scalar response $Y$ given a d-dimensional vector of covariates $X$. First we focus on the population level and show how optimal…
Consider a positive random variable of interest Y depending on a covariate X, and a random observation time T independent of Y given X. Assume that the only knowledge available about Y is its current status at time T: \delta = 1_{Y \leq T}.…
The study of multivariate extremes is dominated by multivariate regular variation, although it is well known that this approach does not provide adequate distinction between random vectors whose components are not always simultaneously…
Models based on assumptions of multivariate regular variation and hidden regular variation provide ways to describe a broad range of extremal dependence structures when marginal distributions are heavy tailed. Multivariate regular variation…
In this article, the estimation of reliability of a system is discussed $p(y<x)$ when strength, $X$, and stress, $Y$, are two independent exponential distribution with different scale parameters when the available data are type II Censored…
In this article we discuss estimation of the common variance of several normal populations with tree order restricted means. We discuss the asymptotic properties of the maximum likelihood estimator of the variance as the number of…
We propose a new method for estimating the extreme quantiles for a function of several dependent random variables. In contrast to the conventional approach based on extreme value theory, we do not impose the condition that the tail of the…
We present a symbolic machinery that admits both probabilistic and causal information about a given domain and produces probabilistic statements about the effect of actions and the impact of observations. The calculus admits two types of…
Conditionally specified models are often used to describe complex multivariate data. Such models assume implicit structures on the extremes. So far, no methodology exists for calculating extremal characteristics of conditional models since…
The Adaptive Multilevel Splitting algorithm is a very powerful and versatile iterative method to estimate the probability of rare events, based on an interacting particle systems. In an other article, in a so-called idealized setting, the…
Bivariate partial-sums discrete probability distributions are defined. The question of the existence of a limit distribution for iterated partial summations is solved for finite-support bivariate distributions which satisfy conditions under…
This paper proposes a new approach to estimating the distribution of a response variable conditioned on observing some factors. The proposed approach possesses desirable properties of flexibility, interpretability, tractability and…