Related papers: A Stein characterisation of the generalized hyperb…
One of the key ingredients to successfully apply Stein's method for distributional approximation are solutions to the Stein equations and their derivatives. Using Barbour's generator approach, one can solve for the solutions to the Stein…
For any discrete target distribution, we exploit the connection between Markov chains and Stein's method via the generator approach and express the solution of Stein's equation in terms of expected hitting time. This yields new upper bounds…
Let $Y$ be a standard Gamma(k) distributed random variable, $k>0$, and let $X$ be an independent positive random variable. We prove that if $X$ has a hyperbolically monotone density of order $k$ ($HM_k$), then the distributions of $Y\cdot…
A multicanonical formalism is introduced to describe statistical equilibrium of complex systems exhibiting a hierarchy of time and length scales, where the hierarchical structure is described as a set of nested "internal heat reservoirs"…
In Stochastic Thermodynamics, heat is a random variable with a probability distribution associated. Studies of the distribution of heat are mostly in the overdamped regime and in one dimension. Here we solve the heat distribution in the…
A new class of distributional transformations is introduced, characterized by equations relating function weighted expectations of test functions on a given distribution to expectations of the transformed distribution on the test function's…
We prove lower bounds on the number of samples needed to privately estimate the covariance matrix of a Gaussian distribution. Our bounds match existing upper bounds in the widest known setting of parameters. Our analysis relies on the…
A discrete-time stochastic process derived from a model of basketball is used to generalize any discrete distribution. The generalized distributions can have one or two more parameters than the parent distribution. Those derived from…
In this paper we study a wide and flexible family of discrete distributions, the so-called generalized negative binomial (GNB) distributions that are mixed Poisson distributions in which the mixing laws belong to the class of generalized…
The generalized harmonic representation of Einstein's equation is manifestly hyperbolic for a large class of gauge conditions. Unfortunately most of the useful gauges developed over the past several decades by the numerical relativity…
This work introduces a new, explicit bound on the Hellinger distance between a continuous random variable and a Gaussian with matching mean and variance. As example applications, we derive a quantitative Hellinger central limit theorem and…
We provide a general result for bounding the difference between point probabilities of integer supported distributions and the translated Poisson distribution, a convenient alternative to the discretized normal. We illustrate our theorem in…
Let F ($\nu$) be the centered Gamma law with parameter $\nu$ > 0 and let us denote by P Y the probability distribution of a random vector Y. We develop a multidimensional variant of the Stein's method for Gamma approximation that allows to…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
Let $h$ be a three times partially differentiable function on $R^n$, let $X=(X_1,\dots,X_n)$ be a collection of real-valued random variables and let $Z=(Z_1,\dots,Z_n)$ be a multivariate Gaussian vector. In this article, we develop Stein's…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…
Due to the skessed distribution, high peak and thick tail and asymmetry of financial return data, it is difficult to describe the traditional distribution. In recent years, generalized autoregressive score (GAS) has been used in many fields…
In this paper, we propose a modification to the density approach to Stein's method for intervals for the unit circle $\mathbb{S}^1$ which is motivated by the differing geometry of $\mathbb{S}^1$ to Euclidean space. We provide an upper bound…
The derivation and application of Stein identities have received considerable research interest in recent years, especially for continuous or discrete-univariate distributions. In this paper, we complement the existing literature by…