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Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…

Statistics Theory · Mathematics 2021-07-02 Mark van der Laan , Zeyi Wang , Lars van der Laan

Logistic regression is a classical model for describing the probabilistic dependence of binary responses to multivariate covariates. We consider the predictive performance of the maximum likelihood estimator (MLE) for logistic regression,…

Statistics Theory · Mathematics 2026-02-20 Hugo Chardon , Matthieu Lerasle , Jaouad Mourtada

We study maximum likelihood estimation (MLE) in the generalized group orbit recovery model, where each observation is generated by applying a random group action and a known, fixed linear operator to an unknown signal, followed by additive…

Statistics Theory · Mathematics 2025-09-30 Sheng Xu , Anderson Ye Zhang , Amit Singer

The paper presents a novel asymptotic distribution for a mle when the log--likelihood is strictly concave in the parameter for all data points; for example, the exponential family. The new asymptotic distribution can be seen as a refinement…

Statistics Theory · Mathematics 2021-06-15 Stephen G Walker

The Latent Block Model (LBM) is a model-based method to cluster simultaneously the $d$ columns and $n$ rows of a data matrix. Parameter estimation in LBM is a difficult and multifaceted problem. Although various estimation strategies have…

Statistics Theory · Mathematics 2020-02-26 Vincent Brault , Christine Keribin , Mahendra Mariadassou

In this paper, we develop asymptotic theories for a class of latent variable models for large-scale multi-relational networks. In particular, we establish consistency results and asymptotic error bounds for the (penalized) maximum…

Statistics Theory · Mathematics 2020-09-01 Zhi Wang , Xueying Tang , Jingchen Liu

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

A two-stage adaptive optimal design is an attractive option for increasing the efficiency of clinical trials. In these designs, based on interim data, the locally optimal dose is chosen for further exploration, which induces dependencies…

Methodology · Statistics 2019-05-24 Zhantao Lin , Nancy Flournoy , William F. Rosenberger

We establish the asymptotic normality of the regression estimator in a fixed-design setting when the errors are given by a field of dependent random variables. The result applies to martingale-difference or strongly mixing random fields. On…

Statistics Theory · Mathematics 2009-07-10 Mohamed El Machkouri , Radu Stoica

We show that the mean-model parameter is always orthogonal to the error distribution in generalized linear models. Thus, the maximum likelihood estimator of the mean-model parameter will be asymptotically efficient regardless of whether the…

Methodology · Statistics 2020-10-08 Alan Huang , Paul J. Rathouz

If the log likelihood is approximately quadratic with constant Hessian, then the maximum likelihood estimator (MLE) is approximately normally distributed. No other assumptions are required. We do not need independent and identically…

Statistics Theory · Mathematics 2012-07-06 Charles J. Geyer

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

Maximum likelihood estimation (MLE) and heuristic predictive estimation (HPE) are two widely used approaches in industrial uncertainty analysis. We review them from the point of view of decision theory, using Bayesian inference as a gold…

Applications · Statistics 2010-09-23 Merlin Keller , Eric Parent , Alberto Pasanisi

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

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…

Statistics Theory · Mathematics 2020-05-04 Trisha Maitra , Sourabh Bhattacharya

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

Suppose that the normal model is used for data $Y_1,\ldots,Y_n$, but that the true distribution is a t-distribution with location and scale parameters $\xi$ and $\sigma$ and $m$ degrees of freedom. The normal model corresponds to…

Methodology · Statistics 2026-03-31 Nils Lid Hjort

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

Most asymptotic results for robust estimates rely on regularity conditions that are difficult to verify in practice. Moreover, these results apply to fixed distribution functions. In the robustness context the distribution of the data…

Statistics Theory · Mathematics 2007-06-13 Matias Salibian-Barrera , Ruben H. Zamar

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