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We investigate the optimization landscape of maximum likelihood estimation (MLE) for the Cavender-Farris-Neyman (CFN) model, a two-state latent tree model fundamental to statistical phylogenetics and the ferromagnetic Ising model. Although…
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…
We study probability density functions that are log-concave. Despite the space of all such densities being infinite-dimensional, the maximum likelihood estimate is the exponential of a piecewise linear function determined by finitely many…
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…
We apply the techniques of stochastic integration with respect to fractional Brownian motion and the theory of regularity and supremum estimation for stochastic processes to study the maximum likelihood estimator (MLE) for the drift…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
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…
A famous characterization theorem due to C.F. Gauss states that the maximum likelihood estimator (MLE) of the parameter in a location family is the sample mean for all samples of all sample sizes if and only if the family is Gaussian. There…
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)…
A key challenge of modern machine learning systems is to achieve Out-of-Distribution (OOD) generalization -- generalizing to target data whose distribution differs from that of source data. Despite its significant importance, the…
Maximum likelihood estimation (MLE) of latent variable models is often recast as the minimization of a free energy functional over an extended space of parameters and probability distributions. This perspective was recently combined with…
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…
In this paper we consider two generalizations of Lancaster's (Review of Economic Studies, 2002) Modified Maximum Likelihood estimator (MMLE) for the panel AR(1) model with fixed effects, arbitrary initial conditions, and strictly exogenous…
We give answer to an open problem regarding consistency of the maximum likelihood estimators (MLEs) in generalized linear mixed models (GLMMs) involving crossed random effects. The solution to the open problem introduces an interesting,…
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…
When estimating a proportion and only a sample of triplets is given, dependencies within the triplets are to be accounted for. Without assuming a distribution for the success count of the triplet, together with the proportion, as second and…
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…
The normalized maximized likelihood (NML) provides the minimax regret solution in universal data compression, gambling, and prediction, and it plays an essential role in the minimum description length (MDL) method of statistical modeling…
In this paper, we consider distributed maximum likelihood estimation (MLE) with dependent quantized data under the assumption that the structure of the joint probability density function (pdf) is known, but it contains unknown deterministic…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…