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We give an asymptotic development of the maximum likelihood estimator (MLE), or any other estimator defined implicitly, in a way which involves the limiting behavior of the score and its higher-order derivatives. This development, which is…

Statistics Theory · Mathematics 2024-04-10 Antoine Lejay , Sara Mazzonetto

The extremes of a stationary time series typically occur in clusters. A primary measure for this phenomenon is the extremal index, representing the reciprocal of the expected cluster size. Both a disjoint and a sliding blocks estimator for…

Statistics Theory · Mathematics 2017-07-14 Betina Berghaus , Axel Bücher

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood…

Computation · Statistics 2014-09-30 Hien D. Nguyen , Ian A. Wood

Maximum likelihood estimators for time-dependent mean functions within Gaussian processes are provided in the context of continuous observations. We find the widest possible class of mean functions for which the likelihood function can be…

Statistics Theory · Mathematics 2025-07-09 Mitsuki Kobayashi , Yuto Nishiwaki , Yasutaka Shimizu , Nobutoki Takaoka

We exploit the asymptotic normality of the extreme value theory (EVT) based estimators of the parameters of a symmetric L\'evy-stable distribution, to construct confidence intervals. The accuracy of these intervals is evaluated through a…

Statistics Theory · Mathematics 2019-04-11 Djamel Meraghni , Louiza Soltane

The maximum likelihood principle is widely used in statistics, and the associated estimators often display good properties. indeed maximum likelihood estimators are guaranteed to be asymptotically efficient under mild conditions. However in…

Statistics Theory · Mathematics 2016-12-01 Christophe Culan , Claude Adnet

In this work, we focus on some conditional extreme risk measures estimation for elliptical random vectors. In a previous paper, we proposed a methodology to approximate extreme quantiles, based on two extremal parameters. We thus propose…

Statistics Theory · Mathematics 2018-07-26 Antoine Usseglio-Carleve

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a long established result. Explicit bounds for the distributional distance between the distribution of the MLE and the normal distribution have recently been obtained for…

Statistics Theory · Mathematics 2016-09-20 Andreas Anastasiou

An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time point is given by a nonobservable Markov chain. In this paper we consider the asymptotic properties of the maximum…

Statistics Theory · Mathematics 2007-06-13 Randal Douc , Eric Moulines , Tobias Ryden

We consider covariance parameter estimation for Gaussian processes with functional inputs. From an increasing-domain asymptotics perspective, we prove the asymptotic consistency and normality of the maximum likelihood estimator. We extend…

Statistics Theory · Mathematics 2024-05-16 Lucas Reding , Andrés F. López-Lopera , François Bachoc

In this paper, we consider asymptotics of the optimal value and the optimal solutions of parametric minimax estimation problems. Specifically, we consider estimators of the optimal value and the optimal solutions in a sample minimax problem…

Statistics Theory · Mathematics 2025-04-16 Mika Meitz , Alexander Shapiro

In this paper, we study the asymptotic normality of the conditional maximum likelihood (ML) estimators for the truncated regression model and the Tobit model. We show that under the general setting assumed in his book, the conjectures made…

Statistics Theory · Mathematics 2008-02-06 Chunlin Wang

We discuss the use of likelihood asymptotics for inference on risk measures in univariate extreme value problems, focusing on estimation of high quantiles and similar summaries of risk for uncertainty quantification. We study whether…

Methodology · Statistics 2021-01-28 Léo R. Belzile , Anthony C. Davison

The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…

Statistics Theory · Mathematics 2023-02-14 Shota Takeishi

This paper is devoted to the estimation of a vector $\bm {\theta}$ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator…

Statistics Theory · Mathematics 2008-12-18 Jean-Michel Billiot , Jean-François Coeurjolly , Rémy Drouilhet

\cite{HillMotegi2017} present a new general asymptotic theory for the maximum of a random array $\{\mathcal{X}_{n}(i)$ $:$ $1$ $\leq $ $i$ $\leq $ $\mathcal{L}\}_{n\geq 1}$, where each $\mathcal{X}_{n}(i)$ is assumed to converge in…

Statistics Theory · Mathematics 2018-02-27 Jonathan B. Hill

We prove uniqueness of the maximum likelihood estimator for the class of k-monotone densities.

Statistics Theory · Mathematics 2010-01-13 Arseni Seregin

For an affine two factor model, we study the asymptotic properties of the maximum likelihood and least squares estimators of some appearing parameters in the so-called subcritical (ergodic) case based on continuous time observations. We…

Statistics Theory · Mathematics 2014-06-17 Matyas Barczy , Leif Doering , Zenghu Li , Gyula Pap

We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…

Statistics Theory · Mathematics 2025-07-24 Claudio Agostinelli , Ayanendranath Basu , Giulia Bertagnolli , Arun Kumar Kuchibhotla

Models with multiple change points are used in many fields; however, the theoretical properties of maximum likelihood estimators of such models have received relatively little attention. The goal of this paper is to establish the asymptotic…

Statistics Theory · Mathematics 2011-02-28 Heping He , Thomas A. Severini