Related papers: An estimator for Poisson means whose relative erro…
Two new information-theoretic methods are introduced for establishing Poisson approximation inequalities. First, using only elementary information-theoretic techniques it is shown that, when $S_n=\sum_{i=1}^nX_i$ is the sum of the (possibly…
In this work, we introduce a novel estimator of the predictive risk with Poisson data, when the loss function is the Kullback-Leibler divergence, in order to define a regularization parameter's choice rule for the Expectation Maximization…
Existing algorithms for subgroup discovery with numerical targets do not optimize the error or target variable dispersion of the groups they find. This often leads to unreliable or inconsistent statements about the data, rendering practical…
Many statistical applications involve models for which it is difficult to evaluate the likelihood, but from which it is relatively easy to sample. Approximate Bayesian computation is a likelihood-free method for implementing Bayesian…
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…
For real symmetric matrices that are accessible only through matrix vector products, we present Monte Carlo estimators for computing the diagonal elements. Our probabilistic bounds for normwise absolute and relative errors apply to Monte…
This paper is concerned with making Bayesian inference from data that are assumed to be drawn from a Bingham distribution. A barrier to the Bayesian approach is the parameter-dependent normalising constant of the Bingham distribution,…
The goal of this paper is to show that a single robust estimator of the mean of a multivariate Gaussian distribution can enjoy five desirable properties. First, it is computationally tractable in the sense that it can be computed in a time…
The problem of estimating a complex measure made up by a linear combination of Dirac distributions centered on points of the complex plane from a finite number of its complex moments affected by additive i.i.d. Gaussian noise is considered.…
We use bias-reduced estimators of high quantiles, of heavy-tailed distributions, to introduce a new estimator of the mean in the case of infinite second moment. The asymptotic normality of the proposed estimator is established and checked,…
Compound Poisson distributions have been employed by many authors to fit experimental data, typically via the method of moments or maximum likelihood estimation. We propose a new technique and apply it to several sets of published data. It…
This note analyzes properties of the median $\nu$ of the Poisson distribution of order $k$. Given a value for the median in the interval $\nu\in[1,k]$, an equation to calculate the corresponding value of the rate parameter $\lambda$ is…
The bias of an estimator is defined as the difference of its expected value from the parameter to be estimated, where the expectation is with respect to the model. Loosely speaking, small bias reflects the desire that if an experiment is…
A new approach of obtaining stratified random samples from statistically dependent random variables is described. The proposed method can be used to obtain samples from the input space of a computer forward model in estimating expectations…
We propose a novel approach to the problem of mutual information (MI) estimation via introducing a family of estimators based on normalizing flows. The estimator maps original data to the target distribution, for which MI is easier to…
This paper addresses the following question: given a sample of i.i.d. random variables with finite variance, can one construct an estimator of the unknown mean that performs nearly as well as if the data were normally distributed? One of…
The missing mass refers to the proportion of data points in an unknown population of classifier inputs that belong to classes not present in the classifier's training data, which is assumed to be a random sample from that unknown…
Following Baraud, Birg\'e and Sart (2017), we pursue our attempt to design a robust universal estimator of the joint ditribution of $n$ independent (but not necessarily i.i.d.) observations for an Hellinger-type loss. Given such…
A generic out-of-sample error estimate is proposed for robust $M$-estimators regularized with a convex penalty in high-dimensional linear regression where $(X,y)$ is observed and $p,n$ are of the same order. If $\psi$ is the derivative of…
Considering the increasing size of available data, the need for statistical methods that control the finite sample bias is growing. This is mainly due to the frequent settings where the number of variables is large and allowed to increase…