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Anomaly estimation, or the problem of finding a subset of a dataset that differs from the rest of the dataset, is a classic problem in machine learning and data mining. In both theoretical work and in applications, the anomaly is assumed to…

Machine Learning · Computer Science 2021-06-14 Uthsav Chitra , Kimberly Ding , Jasper C. H. Lee , Benjamin J. Raphael

Estimation of autocorrelations and spectral densities is of fundamental importance in many fields of science, from identifying pulsar signals in astronomy to measuring heart beats in medicine. In circumstances where one is interested in…

Methodology · Statistics 2013-01-22 C. H. Fleming , J. M. Calabrese

We study multivariate Gaussian statistical models whose maximum likelihood estimator (MLE) is a rational function of the observed data. We establish a one-to-one correspondence between such models and the solutions to a nonlinear…

Algebraic Geometry · Mathematics 2025-09-04 Carlos Améndola , Lukas Gustafsson , Kathlén Kohn , Orlando Marigliano , Anna Seigal

When in a full exponential family the maximum likelihood estimate (MLE) does not exist, the MLE may exist in the Barndorff-Nielsen completion of the family. We propose a practical algorithm for finding the MLE in the completion based on…

Statistics Theory · Mathematics 2009-01-06 Charles J. Geyer

The minimum number of observations such that the maximum likelihood estimator in a Gaussian graphical model exists with probability one is called the maximum likelihood threshold of the underlying graph G. The natural algebraic relaxation…

Combinatorics · Mathematics 2017-05-24 Grigoriy Blekherman , Rainer Sinn

Boltzmann machines (BMs) are a class of binary neural networks for which there have been numerous proposed methods of estimation. Recently, it has been shown that in the fully visible case of the BM, the method of maximum pseudolikelihood…

Computation · Statistics 2014-09-30 Hien D. Nguyen , Ian A. Wood

We analyze the problem of maximum likelihood estimation for Gaussian distributions that are multivariate totally positive of order two (MTP2). By exploiting connections to phylogenetics and single-linkage clustering, we give a simple proof…

Methodology · Statistics 2018-05-29 Steffen Lauritzen , Caroline Uhler , Piotr Zwiernik

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised.…

Statistical Finance · Quantitative Finance 2016-10-11 F Blasques , P Gorgi , S Koopman , O Wintenberger

Most statistical software packages implement numerical strategies for computation of maximum likelihood estimates in random effects models. Little is known, however, about the algebraic complexity of this problem. For the one-way layout…

Statistics Theory · Mathematics 2013-05-07 Elizabeth Gross , Mathias Drton , Sonja Petrović

This paper investigates the asymptotic distribution of the maximum-likelihood estimate (MLE) in multinomial logistic models in the high-dimensional regime where dimension and sample size are of the same order. While classical large-sample…

Statistics Theory · Mathematics 2023-05-30 Kai Tan , Pierre C. Bellec

As is the case for many curved exponential families, the computation of maximum likelihood estimates in a multivariate normal model with a Kronecker covariance structure is typically carried out with an iterative algorithm, specifically, a…

Statistics Theory · Mathematics 2024-08-28 Mathias Drton , Alexandros Grosdos , Andrew McCormack

The choice of free parameters in network models is subjective, since it depends on what topological properties are being monitored. However, we show that the Maximum Likelihood (ML) principle indicates a unique, statistically rigorous…

Disordered Systems and Neural Networks · Physics 2008-08-07 Diego Garlaschelli , Maria I. Loffredo

We are concerned here with the likelihood ratio statistics in two exponential random graph models -- the $\beta$-model and the Bradley-Terry model, in which the degree sequence on an undirected graph and the out-degree sequence on a…

Statistics Theory · Mathematics 2021-05-03 Ting Yan , Yuanzhang Li , Jinfeng Xu , Yaning Yang , Ji Zhu

We present new results for consistency of maximum likelihood estimators with a focus on multivariate mixed models. Our theory builds on the idea of using subsets of the full data to establish consistency of estimators based on the full…

Statistics Theory · Mathematics 2019-02-13 Karl Oskar Ekvall , Galin L. Jones

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 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 estimation of $\beta$ for the nonlinear model $y = f(X\sp{\top}\beta) + \epsilon$ when $f$ is a nonlinear transformation that is known, $\beta$ has sparse nonzero coordinates, and the number of observations can be much smaller…

Statistics Theory · Mathematics 2009-10-15 Zhiyi Chi

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

This paper generalizes asymptotic properties obtained in the observation-driven times series models considered by \cite{dou:kou:mou:2013} in the sense that the conditional law of each observation is also permitted to depend on the…

Statistics Theory · Mathematics 2015-06-08 Randal Douc , François Roueff , Tepmony Sim

With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an…

Computation · Statistics 2017-08-10 Christian S. Schmid , Bruce A. Desmarais