Related papers: Asymptotic inversion of the binomial and negative …
The histogram is an analysis tool in widespread use within many sciences, with high energy physics as a prime example. However, there exists an inherent bias in the choice of binning for the histogram, with different choices potentially…
Smooth Estimation of probability density and distribution functions from its sample is an attractive and an important problem that has applications in several fields such as, business, medicine, and environment. This article introduces a…
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided its existence is assumed. We derive exact tail asymptotics…
We study certain resonance-counting functions for potential scattering on infinite cylinders or half-cylinders. Under certain conditions on the potential, we obtain asymptotics of the counting functions, with an explicit formula for the…
The article is devoted to Beta and Gamma functions of Cayley-Dickson numbers. It is shown that there are specific features in comparison with the complex case. These functions serve as examples of meromorphic functions of Cayley-Dickson…
In this paper we consider suitable families of power series distributed random variables, and we study their asymptotic behavior in the fashion of large (and moderate) deviations. We also present two examples of fractional counting…
Estimating nonlinear functionals of probability distributions from samples is a fundamental statistical problem. The "plug-in" estimator obtained by applying the target functional to the empirical distribution of samples is biased.…
This is an expository note on useful expressions for the density function of a product of independent random variables where each variable has a Beta distribution.
We study asymptotic behaviour of stochastic approximation procedures with three main characteristics: truncations with random moving bounds, a matrix valued random step-size sequence, and a dynamically changing random regression function.…
In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit…
We propose a new method for obtaining complete asymptotic expansions in a systematic manner, which is suitable for counting sequences of various graph families in dense regime. The core idea is to encode the two-dimensional array of…
Prediction of outstanding claims has been done via nonparametric models (chain ladder), semiparametric models (overdispersed poisson) or fully parametric models. In this paper, we propose models based on negative binomial distributions for…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…
In this work we introduce a new polynomial representation of the Bernoulli numbers in terms of polynomial sums allowing on the one hand a more detailed understanding of their mathematical structure and on the other hand provides a…
Fixed effect estimators of nonlinear panel data models suffer from the incidental parameter problem. This leads to two undesirable consequences in applied research: (1) point estimates are subject to large biases, and (2) confidence…
Standard nonlinear regression is commonly used when modeling indifference points due to its ability to closely follow observed data, resulting in a good model fit. However, standard nonlinear regression currently lacks a reasonable…
Bifurcations of self-similar solutions for reversing interfaces are studied in the slow diffusion equation with strong absorption. The self-similar solutions bifurcate from the time-independent solutions for standing interfaces. We show…
In this paper we consider a variety of procedures for numerical statistical inference in the family of univariate and multivariate stable distributions. In connection with univariate distributions (i) we provide approximations by finite…