Related papers: Asymptotic exponential bounds for MLE deviation un…

The term \emph{moderate deviations} is often used in the literature to mean a class of large deviation principles that, in some sense, fill the gap between a convergence in probability to zero (governed by a large deviation principle) and a…

The paper offers a novel unified approach to studying the accuracy of parameter estimation by the quasi likelihood method. Important features of the approach are: (1) The underlying model {is not assumed to be parametric}. (2) No conditions…

We deduce in this short report the non-asymptotic for exponential tail of distribution for sums of independent centered random variables.

Delattre et al. (2013) considered a system of stochastic differential equations (SDEs) in a random effects setup. Under the independent and identical (iid) situation, and assuming normal distribution of the random effects, they established…

In this article we investigate consistency and asymptotic normality of the maximum likelihood and the posterior distribution of the parameters in the context of state space stochastic differential equations (SDEs). We then extend our…

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…

The problem of sampling according to the probability distribution minimizing a given free energy, using interacting particles unadjusted kinetic Langevin Monte Carlo, is addressed. In this setting, three sources of error arise, related to…

MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a…

This paper provides a detailed description for the asymptotics of exponential functionals of random walks with light/heavy tails. We give the convergence rate based on the key observation that the asymptotics depends on the sample paths…

For affine stochastic differential equation with uniformly distributed time delay the local asymptotic properties of the likelihood function are studied. Local asymptotic normality, local asymptotic mixed normality, periodic local…

We derive sharp non - asymptotical Lebesgue - Riesz as well as Grand Lebesgue Space norm estimations for different norms of matrix martingales through these norms for the correspondent martingale differences and through the entropic…

We establish some new non-asymptotical lower bounds for deviation of regular unbiased estimation of unknown parameter from its true value in different norms, alike the classical Rao-Kramer's inequality. We show that if the new norm is…

This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…

Expectile bears some interesting properties in comparison to the industry wide expected shortfall in terms of assessment of tail risk. We study the relationship between expectile and expected shortfall using duality results and the link to…

Nonparametric maximum likelihood estimators (MLEs) in inverse problems often have non-normal limit distributions, like Chernoff's distribution. However, if one considers smooth functionals of the model, with corresponding functionals of the…

In various disordered systems or non-equilibrium dynamical models, the large deviations of some observables have been found to display different scalings for rare values bigger or smaller than the typical value. In the present paper, we…

In this work, we present a generalized methodology for analyzing the convergence of quasi-optimal Taylor and Legendre approximations, applicable to a wide class of parameterized elliptic PDEs with finite-dimensional deterministic and…

Strong consistency and asymptotic normality of the Quasi-Maximum Likelihood Estimator (QMLE) are given for a general class of multidimensional causal processes. For particular cases already studied in the literature (for instance univariate…

We develop asymptotic approximations that can be applied to sequential estimation and inference problems, adaptive randomized controlled trials, and related settings. In batched adaptive settings where the decision at one stage can affect…

Accumulated Local Effect (ALE) is a method for accurately estimating feature effects, overcoming fundamental failure modes of previously-existed methods, such as Partial Dependence Plots. However, ALE's approximation, i.e. the method for…