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Related papers: On the Concentration of the Missing Mass

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We revisit the problem of \emph{missing mass concentration}, developing a new method of estimating concentration of heterogenic sums, in spirit of celebrated Rosenthal's inequality. As a result we slightly improve the state-of-art bounds…

Statistics Theory · Mathematics 2020-05-25 Maciej Skorski

This paper provides further insight into the key concept of missing at random (MAR) in incomplete data analysis. Following the usual selection modelling approach we envisage two models with separable parameters: a model for the response of…

Statistics Theory · Mathematics 2007-06-13 Guobing Lu , John B. Copas

We present a mathematical method to statistically decouple the effects of unknown inclination angles on the mass distribution of exoplanets that have been discovered using radial-velocity techniques. The method is based on the distribution…

Earth and Planetary Astrophysics · Physics 2015-06-05 S. Lopez , J. S. Jenkins

Let $P=(x_1,\ldots,x_n)$ be a population consisting of $n\ge 2$ real numbers whose sum is zero, and let $k <n$ be a positive integer. We sample $k$ elements from $P$ without replacement and denote by $X_P$ the sum of the elements in our…

Probability · Mathematics 2025-03-27 Jianhang Ai , Ondřej Kuželka , Christos Pelekis

A classical problem in statistics is estimating the expected coverage of a sample, which has had applications in gene expression, microbial ecology, optimization, and even numismatics. Here we consider a related extension of this problem to…

Statistics Theory · Mathematics 2013-02-11 Jerrad Hampton , Manuel E. Lladser

Nonprobability (convenience) samples are increasingly sought to reduce the estimation variance for one or more population variables of interest that are estimated using a randomized survey (reference) sample by increasing the effective…

Feature allocation models generalize species sampling models by allowing every observation to belong to more than one species, now called features. Under the popular Bernoulli product model for feature allocation, given $n$ samples, we…

Statistics Theory · Mathematics 2020-09-22 Fadhel Ayed , Marco Battiston , Federico Camerlenghi , Stefano Favaro

The average properties of the well-known Subset Sum Problem can be studied by the means of its randomised version, where we are given a target value $z$, random variables $X_1, \ldots, X_n$, and an error parameter $\varepsilon > 0$, and we…

In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…

Statistics Theory · Mathematics 2025-10-07 Henrik Kaiser

Missing values are ubiquitous in (data) science, with potential detrimental consequences for any statistical analysis. As a consequence, a wealth of methods and theoretical results have been developed in recent years. Still, many questions…

Statistics Theory · Mathematics 2026-03-25 Badr-Eddine Chérief-Abdellatif , Jeffrey Näf

The sample correlation coefficient $R$ plays an important role in many statistical analyses. We study the moments of $R$ under the bivariate Gaussian model assumption, provide a novel approximation for its finite sample mean and connect it…

Statistics Theory · Mathematics 2024-01-23 Daniel Salnikov

We consider studies where multiple measures on an outcome variable are collected over time, but some subjects drop out before the end of follow up. Analyses of such data often proceed under either a 'last observation carried forward' or…

Methodology · Statistics 2022-07-26 Oliver Dukes , David Richardson , Eric Tchetgen Tchetgen

Improving Importance Sampling estimators for rare event probabilities requires sharp approx- imations of the optimal density leading to a nearly zero-variance estimator. This paper presents a new way to handle the estimation of the…

Statistics Theory · Mathematics 2014-01-15 Virgile Caron

The concept of missing at random is central in the literature on statistical analysis with missing data. In general, inference using incomplete data should be based not only on observed data values but should also take account of the…

Methodology · Statistics 2013-06-13 Shaun Seaman , John Galati , Dan Jackson , John Carlin

This paper is concerned with Bayesian inference when the likelihood is analytically intractable but can be unbiasedly estimated. We propose an annealed importance sampling procedure for estimating expectations with respect to the posterior.…

Methodology · Statistics 2014-02-26 M. -N. Tran , C. Strickland , M. K. Pitt , R. Kohn

Models for analyzing multivariate data sets with missing values require strong, often unassessable, assumptions. The most common of these is that the mechanism that created the missing data is ignorable - a twofold assumption dependent on…

Applications · Statistics 2020-02-17 Iavor Bojinov , Natesh Pillai , Donald Rubin

We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…

Probability · Mathematics 2020-02-21 Go Kato

Nested sampling has emerged as a valuable tool for Bayesian analysis, in particular for determining the Bayesian evidence. The method is based on a specific type of random sampling of the likelihood function and prior volume of the…

Instrumentation and Methods for Astrophysics · Physics 2015-05-27 Charles R. Keeton

The concentration of measure phenomenon may be summarized as follows: a function of many weakly dependent random variables that is not too sensitive to any of its individual arguments will tend to take values very close to its expectation.…

Probability · Mathematics 2016-11-18 Aryeh Kontorovich , Maxim Raginsky

In a recent paper, Aldous, Blanc and Curien asked which distributions can be expressed as the distance between two independent random variables on some separable measured metric space. We show that every nonnegative discrete distribution…

Probability · Mathematics 2025-07-22 Renan Gross