Related papers: Asymptotic exponential bounds for MLE deviation un…

We obtain asymptotic approximations for the probability density function of the product of two correlated normal random variables with non-zero means and arbitrary variances. As a consequence, we deduce asymptotic approximations for the…

By using a probabilistic technique based on the exponential change of measure we find a precise tail asymptotic behavior of some perpetuities with distributions close to the Dickman distribution.

We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy and R\'enyi/Tsallis relative distances (including Pearson's…

Approximate Bayesian computation allows for statistical analysis in models with intractable likelihoods. In this paper we consider the asymptotic behaviour of the posterior distribution obtained by this method. We give general results on…

A procedure for asymptotic bias reduction of maximum likelihood estimates of generic estimands is developed. The estimator is realized as a plug-in estimator, where the parameter maximizes the penalized likelihood with a penalty function…

We derive in this short report the exact exponential decreasing tail of distribution for naturel normed sums of independent centered random variables (r.v.), applying the theory of Grand Lebesgue Spaces (GLS). We consider also some…

We discuss in this paper a possibility of constructing a whole class of asymptotic distribution-free tests for testing regularly varying tail distributions. The idea is that we treat the tails of distributions as members of a parametric…

The purpose of this article is to develop a general parametric estimation theory that allows the derivation of the limit distribution of estimators in non-regular models where the true parameter value may lie on the boundary of the…

We give sufficient conditions for the asymptotic normality of linear combinations of order statistics (L-statistics) in the case of simple random samples without replacement. In the first case, restrictions are imposed on the weights of…

We consider the quantum dynamics of a particle on a lattice for large times. Assuming translation invariance, and either discrete or continuous time parameter, the distribution of the ballistically scaled position $Q(t)/t$ converges weakly…

We provide explicit nonasymptotic estimates for the rate of convergence of empirical means of Markov chains, together with a Gaussian or exponential control on the deviations of empirical means. These estimates hold under a "positive…

Much of the theory of estimation for exponential family models, which include exponential-family random graph models (ERGMs) as a special case, is well-established and maximum likelihood estimates in particular enjoy many desirable…

In this paper non-asymptotic moment estimates are derived for tail of distribution for discrete time polynomial martingale by means of martingale differences as a rule in the terms of unconditional and unconditional relative moments and…

Consider semiparametric models that display local asymptotic exponentiality (Ibragimov and Has'minskii (1981)), an asymptotic property of the likelihood associated with discontinuities of densities. Our interest goes to estimation of the…

We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous…

We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general…

Multivariate extreme value theory is concerned with modeling the joint tail behavior of several random variables. Existing work mostly focuses on asymptotic dependence, where the probability of observing a large value in one of the…

We propose a "decomposition method" to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables,…

For sequences of non-lattice weakly dependent random variables, we obtain asymptotic expansions for Large Deviation Principles. These expansions, commonly referred to as strong large deviation results, are in the spirit of Edgeworth…

M-estimation, aka empirical risk minimization, is at the heart of statistics and machine learning: Classification, regression, location estimation, etc. Asymptotic theory is well understood when the loss satisfies some smoothness…