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This paper aims to study a new stochastic order based upon discrete Laplace transforms. By this order, in a setup where the sample size is random, having discrete delta and nabla distributions, we obtain some ordering results involving…
Using the spectral multiplicities of the standard torus, we endow the Laplace eigenspaces with Gaussian probability measures. This induces a notion of random Gaussian Laplace eigenfunctions on the torus ("arithmetic random waves"). We study…
Suppose $\{\widehat\theta_n\colon n\ge1\}$ is a strongly consistent sequence of estimators for a parameter $\theta$, where $\widehat\theta_n$ is based on the first $n$ observations. Consider $Q_\varepsilon$, the number of times…
In this paper, we derive valid Edgeworth expansions for studentized versions of a large class of statistics when the data are generated by a strongly mixing process. Under dependence, the asymptotic variance of such a statistic is given by…
In this paper three new characterizing theorems of exponential distribution are presented. They are based on equidistribution of some functions of order statistics. All of them include the median of sample of size three.
Informative interim adaptations lead to random sample sizes. The random sample size becomes a component of the sufficient statistic and estimation based solely on observed samples or on the likelihood function does not use all available…
In this paper we extend our recent work on two-dimensional (2D) diffusive search-and-capture processes with multiple small targets (narrow capture problems) by considering an asymptotic expansion of the Laplace transformed probability flux…
In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint…
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…
We present an orthogonal expansion for real, function-regulated, second-order random measures over $\mathbb{R}^{d}$ with measure covariance. Such a expansion, which can be seen as a Karhunen-Lo\`eve decomposition, consists in a series of…
We explore some properties of the conditional distribution of an i.i.d. sample under large exceedances of its sum. Thresholds for the asymptotic independance of the summands are observed, in contrast with the classical case when the…
For a regression model, we consider the risk of the maximum likelihood estimator with respect to $\alpha$-divergence, which includes the special cases of Kullback-Leibler divergence, Hellinger distance and $\chi^2$ divergence. The…
Let $(X,d)$ be a geodesic Gromov-hyperbolic space, $o \in X$ a basepoint and $\mu$ a countably supported non-elementary probability measure on $\operatorname{Isom}(X)$. Denote by $z_n$ the random walk on $X$ driven by the probability…
A sum of observations derived by a simple random sampling design from a population of independent random variables is studied. A procedure finding a general term of Edgeworth asymptotic expansion is presented. The Lindeberg condition of…
Consider the task of generating samples from a tilted distribution of a random vector whose underlying distribution is unknown, but samples from it are available. This finds applications in fields such as finance and climate science, and in…
We derive an extended empirical likelihood for parameters defined by estimating equations which generalizes the original empirical likelihood for such parameters to the full parameter space. Under mild conditions, the extended empirical…
We present non-asymptotic two-sided bounds to the log-marginal likelihood in Bayesian inference. The classical Laplace approximation is recovered as the leading term. Our derivation permits model misspecification and allows the parameter…
We introduce a second-order stochastic model to explore the variability in growth of biological shapes with applications to medical imaging. Our model is a perturbation with a random force of the Hamiltonian formulation of the geodesics.…
This manuscript investigates the stochastic comparisons of the second-order statistics from dependent and heterogeneous general semi-parametric family of distributions observations. Some sufficient conditions on the usual stochastic order…
We establish lower bounds on the volume and the surface area of a geometric body using the size of its slices along different directions. In the first part of the paper, we derive volume bounds for convex bodies using generalized…