Related papers: On point estimators for Gamma and Beta distributio…
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research…
Using Stein's method and the Malliavin calculus of variations, we derive explicit estimates for the Gamma approximation of functionals of a Poisson measure. In particular, conditions are presented under which the distribution of a sequence…
Estimation of a deterministic quantity observed in non-Gaussian additive noise is explored via order statistics approach. More specifically, we study the estimation problem when measurement noises either have positive supports or follow a…
We consider goodness-of-fit tests of symmetric stable distributions based on weighted integrals of the squared distance between the empirical characteristic function of the standardized data and the characteristic function of the standard…
In this paper we study the effective degrees of freedom of a general class of reduced rank estimators for multivariate regression in the framework of Stein's unbiased risk estimation (SURE). We derive a finite-sample exact unbiased…
The vanilla method in univariate extreme-value theory consists of fitting the three-parameter Generalized Extreme-Value (GEV) distribution to a sample of block maxima. Despite claims to the contrary, the asymptotic normality of the maximum…
Since the baryon-to-photon ratio "eta" is in some doubt at present, we ignore the constraints on eta from big bang nucleosynthesis (BBN) and fit the three key cosmological parameters (h, Omega_M, eta) to four other observational…
We study the parameter estimation method for linear regression models with possibly skewed stable distributed errors. Our estimation procedure consists of two stages: first, for the regression coefficients, the Cauchy quasi-maximum…
We consider the problem of the estimation of the invariant distribution function of an ergodic diffusion process when the drift coefficient is unknown. The empirical distribution function is a natural estimator which is unbiased, uniformly…
We provide optimal bounds for $\alpha (\beta \circ \gamma \circ \dots )$ in $4$-distributive varieties, as well as some further partial generalizations.
The James-Stein estimator's dominance over maximum likelihood in terms of mean square error (MSE) has been one of the most celebrated results in modern statistics, suggesting that biased estimators can systematically outperform unbiased…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We describe the distribution of frequencies ordered by sample values in a random sample of size $n$ from the two parameter GEM$(\alpha,\theta)$ random discrete distribution on the positive integers. These frequencies are a…
We propose the use of U-statistics to reduce variance for gradient estimation in importance-weighted variational inference. The key observation is that, given a base gradient estimator that requires $m > 1$ samples and a total of $n > m$…
To measure the degree of agreement between two observers that independently classify $n$ subjects within $K$ categories, it is common to use different kappa type coefficients, the most common of which is the $\kappa_C$ coefficient (Cohen's…
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its…
The Beta kernel estimator offers a theoretically superior alternative to the Gaussian kernel for unit interval data, eliminating boundary bias without requiring reflection or transformation. However, its adoption remains limited by the lack…
We employ a parameter-free distribution estimation framework where estimators are random distributions and utilize the Kullback-Leibler (KL) divergence as a loss function. Wu and Vos [J. Statist. Plann. Inference 142 (2012) 1525-1536] show…
The gamma difference distribution is defined as the difference of two gamma distributions, with in general different shape and rate parameters. Starting with knowledge of the corresponding characteristic function, a second order linear…
In a statistical analysis in Particle Physics, nuisance parameters can be introduced to take into account various types of systematic uncertainties. The best estimate of such a parameter is often modeled as a Gaussian distributed variable…