Related papers: Estimates for order statistics in terms of quantil…

We show that several versions of Floyd and Rivest's improved algorithm Select for finding the $k$th smallest of $n$ elements require at most $n+\min\{k,n-k\}+O(n^{1/2}\ln^{1/2}n)$ comparisons on average and with high probability. This…

Let $\{X_{1},\ldots,X_{N_1}\}$ and $\{Y_{1},\ldots,Y_{N_2}\}$ be two sequences of interdependent heterogeneous samples, where for $i=1,\ldots,N_{1},$ $X_{i}\sim \text{Kw-G}(x, \alpha_{i}, \gamma_{i};G)$ and for $i=1,\ldots,N_{2},$…

We obtain bounds to quantify the distributional approximation in the delta method for vector statistics (the sample mean of $n$ independent random vectors) for normal and non-normal limits, measured using smooth test functions. For normal…

Algorithms are proposed for the computation of set-valued quantiles and the values of the lower cone distribution function for bivariate data sets. These new objects make data analysis possible involving an order relation for the data…

For N=1,2,..., let S_N be a simple random sample of size n=n_N from a population A_N of size N, where 0<=n<=N. Then with f_N=n/N, the sampling fraction, and 1_A the inclusion indicator that A is in S_N, for any H a subset of A_N of size k>=…

We address the estimation of conditional quantiles when the covariate is functional and when the order of the quantiles converges to one as the sample size increases. In a first time, we investigate to what extent these large conditional…

Which permutations of a probability distribution on integers minimize variance? Let $X$ be a random variable on a set of integers $\{x_1, \dots, x_N\}$ such that $\mathbb{P}(X_i = x_i) = p_i$, $i \in \{1,\dots,N\}$. Let $(p^{(1)}, \dots,…

We show that generalised extreme value statistics -the statistics of the k-th largest value among a large set of random variables- can be mapped onto a problem of random sums. This allows us to identify classes of non-identical and…

In this paper, we compare extreme order statistics through vector majorization arising from heterogeneous Poisson and geometric random variables. These comparisons are carried out with respect to usual stochastic ordering.

In order to develop certain fractional probabilistic analogues of Taylor's theorem and mean value theorem, we introduce the nth-order fractional equilibrium distribution in terms of the Weyl fractional integral and investigate its main…

For nonnegative random variables with finite means we introduce an analogous of the equilibrium residual-lifetime distribution based on the quantile function. This allows to construct new distributions with support (0,1), and to obtain a…

We study the problem of estimating the mean of a multivariatedistribution based on independent samples. The main result is the proof of existence of an estimator with a non-asymptotic sub-Gaussian performance for all distributions…

Let $X_1, \ldots , X_n$ be mutually independent exponential random variables with distinct hazard rates $\lambda_1, \ldots , \lambda_n > 0$ and let $Y_1, \ldots, Y_n$ be a random sample from the exponential distribution with hazard rate…

By considering a least squares approximation of a given square integrable function f:[0,1]^n --> R by a shifted L-statistic function (a shifted linear combination of order statistics), we define an index which measures the global influence…

Consider a pair of cumulative distribution functions $F$ and $G$, where $F$ is unknown and $G$ is a known reference distribution. Given a sample from $F$, we propose tests to detect the convexity or the concavity of $G^{-1}\circ F$ versus…

A random variable $Y_1$ is said to be smaller than $Y_2$ in the increasing concave stochastic order if $\mathbb{E}[\phi(Y_1)] \leq \mathbb{E}[\phi(Y_2)]$ for all increasing concave functions $\phi$ for which the expected values exist, and…

The Median of Means (MoM) is a mean estimator that has gained popularity in the context of heavy-tailed data. In this work, we analyze its performance in the task of simultaneously estimating the mean of each function in a class…

The factorial moments of the standard Poisson distribution are well known. The present note presents an explicit combinatorial sum for the factorial moments of the Poisson distribution of order $k$. Unlike the standard Poisson distribution…

Let $X,X_1,...,X_n$ be independent identically distributed random variables. In this paper we study the behavior of the concentration functions of the weighted sums $\sum\limits_{k=1}^{n}a_k X_k$ with respect to the arithmetic structure of…

Due to measurement noise, a common problem in in various fields is how to estimate the ratio of two functions. We consider this problem of estimating the ratio of two functions in a nonparametric regression model. Assuming the noise is…