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We propose a general methodology for the construction and analysis of minimax estimators for a wide class of functionals of finite dimensional parameters, and elaborate on the case of discrete distributions, where the alphabet size $S$ is…

Information Theory · Computer Science 2015-03-11 Jiantao Jiao , Kartik Venkat , Yanjun Han , Tsachy Weissman

The density ratio model (DRM) provides a flexible and useful platform for combining information from multiple sources. In this paper, we consider statistical inference under two-sample DRMs with additional parameters defined through and/or…

Statistics Theory · Mathematics 2021-03-01 Meng Yuan , Pengfei Li , Changbao Wu

Spatial-temporal linear model and the corresponding likelihood-based statistical inference are important tools for the analysis of spatial-temporal lattice data. In this paper, we study the asymptotic properties of maximum likelihood…

Statistics Theory · Mathematics 2012-07-27 Xiang Zhang , Yanbing Zheng

In this paper, we investigate the problem of strong approximation of the solutions of stochastic differential equations (SDEs) when the drift coefficient is given in integral form. We investigate its upper error bounds, in terms of the…

Numerical Analysis · Mathematics 2025-11-20 Paweł Przybyłowicz , Michał Sobieraj

We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random…

Information Theory · Computer Science 2017-08-11 Jiantao Jiao , Kartik Venkat , Yanjun Han , Tsachy Weissman

In this article, we introduce the joint maximum a posteriori state path and parameter estimator (JME) for continuous-time systems described by stochastic differential equations (SDEs). This estimator can be applied to nonlinear systems with…

Statistics Theory · Mathematics 2017-04-07 Dimas Abreu Archanjo Dutra , Bruno Otávio Soares Teixeira , Luis Antonio Aguirre

This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…

Statistics Theory · Mathematics 2019-11-01 Nancy Flournoy , Caterina May , Chiara Tommasi

For the univariate current status and, more generally, the interval censoring model, distribution theory has been developed for the maximum likelihood estimator (MLE) and smoothed maximum likelihood estimator (SMLE) of the unknown…

Statistics Theory · Mathematics 2013-06-18 Piet Groeneboom

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with…

Probability · Mathematics 2016-09-29 Joscha Diehl , Peter Friz , Hilmar Mai

We study nonparametric maximum likelihood estimation of a log-concave density function $f_0$ which is known to satisfy further constraints, where either (a) the mode $m$ of $f_0$ is known, or (b) $f_0$ is known to be symmetric about a fixed…

Statistics Theory · Mathematics 2019-05-15 Charles R. Doss , Jon A. Wellner

This paper deals with nonparametric maximum likelihood estimation for Gaussian locally stationary processes. Our nonparametric MLE is constructed by minimizing a frequency domain likelihood over a class of functions. The asymptotic behavior…

Statistics Theory · Mathematics 2011-11-10 Rainer Dahlhaus , Wolfgang Polonik

We study the maximum likehood estimator and least squares estimator for drift parameters of nonlinear reflected stochastic differential equations based on continuous observations. Under some regular conditions, we obtain the consistency and…

Statistics Theory · Mathematics 2022-05-04 Han Yuecai , Zhang Dingwen

We study the problem of parametric estimation for continuously observed stochastic processes driven by additive small fractional Brownian motion with Hurst index 0<H<1/2 and 1/2<H<1. Under some assumptions on the drift coefficient, we…

Statistics Theory · Mathematics 2022-01-04 Shohei Nakajima , Yasutaka Shimizu

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…

Statistics Theory · Mathematics 2015-09-10 János Marcell Benke , Gyula Pap

We consider hidden Markov models indexed by a binary tree where the hidden state space is a general metric space. We study the maximum likelihood estimator (MLE) of the model parameters based only on the observed variables. In both…

Probability · Mathematics 2025-08-20 Julien Weibel

We consider statistics for stochastic evolution equations in Hilbert space with emphasis on stochastic partial differential equations (SPDEs). We observe a solution process under additional measurement errors and want to estimate a real or…

Statistics Theory · Mathematics 2025-05-21 Gregor Pasemann , Markus Reiß

We consider the problem of estimating the joint distribution function of the event time and a continuous mark variable based on censored data. More specifically, the event time is subject to current status censoring and the continuous mark…

Statistics Theory · Mathematics 2011-09-07 Piet Groeneboom , Geurt Jongbloed , Birgit Witte

Maximum likelihood estimation of linear functionals in the inverse problem of deconvolution is considered. Given observations of a random sample from a distribution $P_0\equiv P_{F_0}$ indexed by a (potentially infinite-dimensional)…

Statistics Theory · Mathematics 2019-02-05 Catia Scricciolo

We consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic…

Probability · Mathematics 2013-09-26 Yuliya Mishura , Kostiantyn Ral'chenko , Oleg Seleznev , Georgiy Shevchenko

Parameter estimation for a parabolic linear stochastic partial differential equation in one space dimension is studied observing the solution field on a discrete grid in a fixed bounded domain. Considering an infill asymptotic regime in…

Statistics Theory · Mathematics 2019-11-26 Florian Hildebrandt , Mathias Trabs