Related papers: On Stochastic Comparisons of Order Statistics from…

We express the joint R\'enyi entropy of progressively censored order statistics in terms of an incomplete integral of the hazard function, and provide a simple estimate of the joint R\'enyi entropy of progressively Type-II censored data.…

We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…

We introduce deterministic perturbation schemes for the recently proposed random directions stochastic approximation (RDSA) [17], and propose new first-order and second-order algorithms. In the latter case, these are the first second-order…

This paper considers a family of distributions constructed by a stochastic mixture of the order statistics of a sample of size two. Various properties of the proposed model are studied. We apply the model to extend the exponential and…

Let recall that the term 'k-th extreme' was introduced in a limiting sense. That is, if $X_{r:n}$ denote the r-th order statistic then for fix k, as $n\to\infty$, $X_{n-k+1:n}$ is called the k-th extremes or k-th largest order statistics.…

We generalize the notion of minimax convergence rate. In contrast to the standard definition, we do not assume that the sample size is fixed in advance. Allowing for varying sample size results in time-robust minimax rates and estimators.…

The article considers the multivariate stochastic orders of upper orthants, lower orthants and positive quadrant dependence (PQD) among simple max-stable distributions and their exponent measures. It is shown for each order that it holds…

We propose and analyze a specific asymptotic stochastic order for random processes based on the measure of departure discussed in the literature. As applications, we stochastically compare mixtures of order statistics and record values…

A simple method to produce a random order type is to take the order type of a random point set. We conjecture that many probability distributions on order types defined in this way are heavily concentrated and therefore sample inefficiently…

Under long memory, the limit theorems for normalized sums of random variables typically involve a positive integer called "Hermite rank". There is a different limit for each Hermite rank. From a statistical point of view, however, we argue…

A class of probability distributions is characterized via equalities in law between two order statistics shifted by independent exponential variables. An explicit formula for the quintile function of the identified family of distributions…

The comparison of a parameter in $k$ populations is a classical problem in statistics. Testing for the equality of means or variances are typical examples. Most procedures designed to deal with this problem assume that $k$ is fixed and that…

Let $\mathbf{X}=\{X_{n}\}_{n\geq 1}$ be a sequence of stationary Gaussian variables and suppose that only some of the random variables from $\mathbf{X}$ can be observed. In this paper, by studying the limiting properties of multidimensional…

We consider the classical problem of discrete distribution estimation using i.i.d. samples in a novel scenario where additional side information is available on the distribution. In large alphabet datasets such as text corpora, such side…

We give an order-explicit large deviation bound for the difference between a high-dimensional $U$-statistic and its H\'{a}jek projection. In particular, we show that any $U$-statistic of order $b$ on $n$ observations, with a $d$-dimensional…

Generalized sorting problem, also known as sorting with forbidden comparisons, was first introduced by Huang et al. together with a randomized algorithm which requires $\tilde O(n^{3/2})$ probes. We study this problem with additional…

Exponential varieties arise from exponential families in statistics. These real algebraic varieties have strong positivity and convexity properties, familiar from toric varieties and their moment maps. Among them are varieties of inverses…

In this paper we investigate the top-$k$-selection problem, i.e. determine the largest, second largest, ..., and the $k$-th largest elements, in the dynamic data model. In this model the order of elements evolves dynamically over time. In…

An evolving problem in the field of spatial and ecological statistics is that of preferential sampling, where biases may be present due to a relationship between sample data locations and a response of interest. This field of research bears…

It is well known that a random vector with given marginal distributions is comonotonic if and only if it has the largest sum with respect to the convex order [ Kaas, Dhaene, Vyncke, Goovaerts, Denuit (2002), A simple geometric proof that…