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Estimating model parameters is a crucial step in mathematical modelling and typically involves minimizing the disagreement between model predictions and experimental data. This calibration data can change throughout a study, particularly if…

Quantitative Methods · Quantitative Biology 2023-11-03 Tyler Cassidy

This paper presents a tractable sufficient condition for the consistency of maximum likelihood estimators (MLEs) in partially observed diffusion models, stated in terms of stationary distribution of the associated fully observed diffusion,…

Statistics Theory · Mathematics 2024-12-10 Sergey Nadtochiy , Yuan Yin

The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…

Data Analysis, Statistics and Probability · Physics 2018-12-03 Anthony Vella

Linear birth-and-death processes (LBDPs) are foundational stochastic models in population dynamics, evolutionary biology, and hematopoiesis. Estimating parameters from discretely observed data is computationally demanding due to irregular…

Computation · Statistics 2025-08-26 Xiaochen Long , Marek Kimmel

We study mixture of linear regression (random coefficient) models, which capture population heterogeneity by allowing the regression coefficients to follow an unknown distribution $G^*$. In contrast to common parametric methods that fix the…

Methodology · Statistics 2025-07-01 Hansheng Jiang , Adityanand Guntuboyina

In the last decade, there has been a growing interest to use Wishart processes for modelling, especially for financial applications. However, there are still few studies on the estimation of its parameters. Here, we study the Maximum…

Statistics Theory · Mathematics 2016-04-18 Aurélien Alfonsi , Ahmed Kebaier , Clément Rey

Distributional regression aims to find the best candidate in a given parametric family of conditional distributions to model a given dataset. As each candidate in the distribution family can be identified by the corresponding distribution…

Statistics Theory · Mathematics 2026-05-18 Gitte Kremling , Gerhard Dikta

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

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

This paper uses the invariance principle to solve the incidental parameter problem of [Econometrica 16 (1948) 1--32]. We seek group actions that preserve the structural parameter and yield a maximal invariant in the parameter space with…

Statistics Theory · Mathematics 2009-09-04 Marcelo J. Moreira

This paper considers maximum likelihood (ML) estimation in a large class of models with hidden Markov regimes. We investigate consistency of the ML estimator and local asymptotic normality for the models under general conditions which allow…

Statistics Theory · Mathematics 2021-12-07 Demian Pouzo , Zacharias Psaradakis , Martin Sola

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

While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood…

Statistics Theory · Mathematics 2016-09-29 Andreas Anastasiou , Gesine Reinert

We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale…

Statistics Theory · Mathematics 2025-07-21 Guanfu Liu , Pengfei Li , Yukun Liu , Xiaolong Pu

In finite mixtures of location-scale distributions, if there is no constraint or penalty on the parameters, then the maximum likelihood estimator does not exist because the likelihood is unbounded. To avoid this problem, we consider a…

Statistics Theory · Mathematics 2011-03-04 Kentaro Tanaka

We construct the maximum likelihood estimator (MLE) of the unknown drift parameter $\theta\in \mathbb{R}$ in the linear model $X_t=\theta t+\sigma B^{H_1}(t)+B^{H_2}(t),\;t\in[0,T],$ where $B^{H_1}$ and $B^{H_2}$ are two independent…

Probability · Mathematics 2015-06-16 Yuliya Mishura

Due to its heavy-tailed and fully parametric form, the multivariate generalized Gaussian distribution (MGGD) has been receiving much attention for modeling extreme events in signal and image processing applications. Considering the…

Applications · Statistics 2017-02-27 F. Pascal , L. Bombrun , J. Y. Tourneret , Y. Berthoumieu

We study the maximal displacement of branching random walks in a class of time inhomogeneous environments. Specifically, binary branching random walks with Gaussian increments will be considered, where the variances of the increments change…

Probability · Mathematics 2011-12-07 Ofer Zeitouni , Ming Fang

We consider a jump-type Cox--Ingersoll--Ross (CIR) process driven by a standard Wiener process and a subordinator, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate. We distinguish three cases:…

Statistics Theory · Mathematics 2018-06-08 Matyas Barczy , Mohamed Ben Alaya , Ahmed Kebaier , Gyula Pap

We prove the asymptotic properties of the maximum likelihood estimator (MLE) in time-varying transition probability (TVTP) regime-switching models. This class of models extends the constant regime transition probability in Markov-switching…

Econometrics · Economics 2021-12-06 Chaojun Li , Yan Liu