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Estimation of the mean vector and covariance matrix is of central importance in the analysis of multivariate data. In the framework of generalized linear models, usually the variances are certain functions of the means with the normal…

Methodology · Statistics 2023-01-25 Anupam Kundu , Mohsen Pourahmadi

This paper aims to examine the characteristics of the posterior distribution of covariance/precision matrices in a "large $p$, large $n$" scenario, where $p$ represents the number of variables and $n$ is the sample size. Our analysis…

Statistics Theory · Mathematics 2026-02-02 Partha Sarkar , Kshitij Khare , Malay Ghosh , Matt P. Wand

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

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

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

We investigate the asymptotic distributions of coordinates of regression M-estimates in the moderate $p/n$ regime, where the number of covariates $p$ grows proportionally with the sample size $n$. Under appropriate regularity conditions, we…

Statistics Theory · Mathematics 2016-12-20 Lihua Lei , Peter J. Bickel , Noureddine El Karoui

In regression models for spatial data, it is often assumed that the marginal effects of covariates on the response are constant over space. In practice, this assumption might often be questionable. In this article, we show how a Gaussian…

Methodology · Statistics 2020-11-13 Jakob A. Dambon , Fabio Sigrist , Reinhard Furrer

We suggest an iterative approach to computing K-step maximum likelihood estimates (MLE) of the parametric components in semiparametric models based on their profile likelihoods. The higher order convergence rate of K-step MLE mainly depends…

Statistics Theory · Mathematics 2007-08-23 Guang Cheng

The aim of this note is to state a couple of general results about the properties of the penalized maximum likelihood estimators (pMLE) and of the posterior distribution for parametric models in a non-asymptotic setup and for possibly large…

Statistics Theory · Mathematics 2022-12-13 Vladimir Spokoiny

Many proposals have emerged as alternatives to the Heckman selection model, mainly to address the non-robustness of its normal assumption. The 2001 Medical Expenditure Panel Survey data is often used to illustrate this non-robustness of the…

Methodology · Statistics 2021-04-02 Fernando de S. Bastos , Wagner Barreto-Souza , Marc G. Genton

This paper studies binary logistic regression for rare events data, or imbalanced data, where the number of events (observations in one class, often called cases) is significantly smaller than the number of nonevents (observations in the…

Machine Learning · Statistics 2020-06-02 HaiYing Wang

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

The stationary distribution of allele frequencies under a variety of Wright--Fisher $k$-allele models with selection and parent independent mutation is well studied. However, the statistical properties of maximum likelihood estimates of…

Applications · Statistics 2009-10-12 Erkan Ozge Buzbas , Paul Joyce

We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons.…

Methodology · Statistics 2025-03-20 Pinjun Dong , Ruijian Han , Binyan Jiang , Yiming Xu

Consider a set of categorical variables $\mathcal{P}$ where at least one, denoted by $Y$, is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the…

Methodology · Statistics 2019-12-04 Wei Jing , Michail Papathomas

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 is a popular method in statistical inference. As a way of assessing the accuracy of the maximum likelihood estimate (MLE), the calculation of the covariance matrix of the MLE is of great interest in practice.…

Statistics Theory · Mathematics 2014-05-08 Xumeng Cao

Motivated by recent works on the high-dimensional logistic regression, we establish that the existence of the maximum likelihood estimate exhibits a phase transition for a wide range of generalized linear models with binary outcome and…

Statistics Theory · Mathematics 2020-12-18 Wenpin Tang , Yuting Ye

We study maximum likelihood estimation in Gaussian graphical models from a geometric point of view. An algebraic elimination criterion allows us to find exact lower bounds on the number of observations needed to ensure that the maximum…

Statistics Theory · Mathematics 2012-05-30 Caroline Uhler

Inspired by applications to theories of coding and communication in networks of nervous tissue, we study maximum entropy distributions on weighted graphs with a given expected degree sequence. These distributions are characterized by…

Statistics Theory · Mathematics 2018-12-18 Christopher Hillar , Andre Wibisono