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It is well known that, under standard regularity conditions, the maximum likelihood estimator (MLE) satisfies a central limit theorem and converges in distribution to a Gaussian random variable as the sample size grows. This paper…

Information Theory · Computer Science 2026-05-26 Leighton P. Barnes , Alex Dytso

Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…

Statistics Theory · Mathematics 2022-06-08 Pragya Sur , Emmanuel J. Candes

In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to…

Applications · Statistics 2015-06-19 Achraf Mallat , Sinan Gezici , Davide Dardari , Christophe Craeye , Luc Vandendorpe

The problem of estimation of density functionals like entropy and mutual information has received much attention in the statistics and information theory communities. A large class of estimators of functionals of the probability density…

Statistics Theory · Mathematics 2013-03-05 Kumar Sricharan , Dennis Wei , Alfred O. Hero

Maximum pseudolikelihood (MPL) estimators are useful alternatives to maximum likelihood (ML) estimators when likelihood functions are more difficult to manipulate than their marginal and conditional components. Furthermore, MPL estimators…

Methodology · Statistics 2017-08-30 Hien D. Nguyen

Finite mixture models are widely used in econometric analyses to capture unobserved heterogeneity. This paper shows that maximum likelihood estimation of finite mixtures of parametric densities can suffer from substantial finite-sample bias…

Methodology · Statistics 2026-02-04 Raphaël Langevin

The aim of this paper is to study the asymptotic properties of the maximum likelihood estimator (MLE) of the drift coefficient for fractional stochastic heat equation driven by an additive space-time noise. We consider the traditional for…

Probability · Mathematics 2019-04-25 Igor Cialenco , Francisco Delgado-Vences , Hyun-Jung Kim

Maximum likelihood estimation (MLE) is a fundamental computational problem in statistics. In this paper, MLE for statistical models with discrete data is studied from an algebraic statistics viewpoint. A reformulation of the MLE problem in…

Statistics Theory · Mathematics 2014-05-27 Jose Israel Rodriguez

We study nonparametric estimation of the sub-distribution functions for current status data with competing risks. Our main interest is in the nonparametric maximum likelihood estimator (MLE), and for comparison we also consider a simpler…

Statistics Theory · Mathematics 2008-06-20 Piet Groeneboom , Marloes H. Maathuis , Jon A. Wellner

We study the uniform convergence rate of the nonparametric maximum likelihood estimator (MLE) for the sub-distribution functions in the current status data with competing risks model. It is known that the MLE have $L^2$-norm convergence…

Statistics Theory · Mathematics 2019-09-16 Sergey V. Malov

We consider the problem of estimating the distribution function, the density and the hazard rate of the (unobservable) event time in the current status model. A well studied and natural nonparametric estimator for the distribution function…

Statistics Theory · Mathematics 2010-01-13 Piet Groeneboom , Geurt Jongbloed , Birgit I. Witte

The behavior of maximum likelihood estimates (MLEs) and the likelihood ratio statistic in a family of problems involving pointwise nonparametric estimation of a monotone function is studied. This class of problems differs radically from the…

Statistics Theory · Mathematics 2009-09-29 Moulinath Banerjee

Determinantal point processes (DPPs) have wide-ranging applications in machine learning, where they are used to enforce the notion of diversity in subset selection problems. Many estimators have been proposed, but surprisingly the basic…

Statistics Theory · Mathematics 2017-07-25 Victor-Emmanuel Brunel , Ankur Moitra , Philippe Rigollet , John Urschel

The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…

Statistics Theory · Mathematics 2026-03-10 Somnath Mandal , Lakshmi Kanta Patra

Maximum-likelihood estimation (MLE) is arguably the most important tool for statisticians, and many methods have been developed to find the MLE. We present a new inequality involving posterior distributions of a latent variable that holds…

Statistics Theory · Mathematics 2019-12-10 Niels Lundtorp Olsen

We study the problem of estimating a rank-1 additive deformation of a Gaussian tensor according to the \emph{maximum-likelihood estimator} (MLE). The analysis is carried out in the sparse setting, where the underlying signal has a support…

Information Theory · Computer Science 2021-01-26 Luca Corinzia , Paolo Penna , Wojciech Szpankowski , Joachim M. Buhmann

We study approximate maximum likelihood estimators (MLEs) for the parameters of the widely used Heston stock and volatility stochastic differential equations (SDEs). We compute explicit closed form estimators maximizing the discretized…

Probability · Mathematics 2015-06-19 Robert Azencott , Yutheeka Gadhyan

Empirical economic research frequently applies maximum likelihood estimation in cases where the likelihood function is analytically intractable. Most of the theoretical literature focuses on maximum simulated likelihood (MSL) estimators,…

Econometrics · Economics 2019-08-13 Michael Griebel , Florian Heiss , Jens Oettershagen , Constantin Weiser

We give a thorough description of the asymptotic property of the maximum likelihood estimator (MLE) of the skewness parameter of a Skew Brownian Motion (SBM). Thanks to recent results on the Central Limit Theorem of the rate of convergence…

Statistics Theory · Mathematics 2023-02-07 Antoine Lejay , Sara Mazzonetto

We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…

Statistics Theory · Mathematics 2020-07-10 Elina Robeva , Bernd Sturmfels , Ngoc Tran , Caroline Uhler