Related papers: Maximum likelihood estimation for left-truncated l…
A striking result of [Acharya et al. 2017] showed that to estimate symmetric properties of discrete distributions, plugging in the distribution that maximizes the likelihood of observed multiset of frequencies, also known as the profile…
We study nonparametric maximum likelihood estimation for two classes of multivariate distributions that imply strong forms of positive dependence; namely log-supermodular (MTP$_2$) distributions and log-$L^\#$-concave (LLC) distributions.…
Large Language Models (LLMs) have shown impressive abilities in many applications. When a concrete and precise answer is desired, it is important to have a quantitative estimation of the potential error rate. However, this can be…
We derive a novel variational expectation maximization approach based on truncated posterior distributions. Truncated distributions are proportional to exact posteriors within subsets of a discrete state space and equal zero otherwise. The…
We consider nonparametric maximum-likelihood estimation of a log-concave density in case of interval-censored, right-censored and binned data. We allow for the possibility of a subprobability density with an additional mass at $+\infty$,…
Gradually Truncated Log-normal distribution - Size distribution of firms Abstract Many natural and economical phenomena are described through power law or log- normal distributions. In these cases, probability decreases very slowly with…
We develop and analyze methods for computing provably optimal {\em maximum a posteriori} (MAP) configurations for a subclass of Markov random fields defined on graphs with cycles. By decomposing the original distribution into a convex…
Three types of explicit estimators are proposed here to estimate the loss rates of the links in a network of the tree topology. All of them are derived by the maximum likelihood principle and proved to be either asymptotic unbiased or…
This study aims to introduce a new lifetime distribution, called the record-based transformed log-logistic distribution, to the literature. We obtain this distribution using a record-based transformation map based on the distributions of…
Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from non-linear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
In this paper, we study two problems: (1) estimation of a $d$-dimensional log-concave distribution and (2) bounded multivariate convex regression with random design with an underlying log-concave density or a compactly supported…
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,…
Inference is typically intractable in high-treewidth undirected graphical models, making maximum likelihood learning a challenge. One way to overcome this is to restrict parameters to a tractable set, most typically the set of…
One of the most common anticipated difficulties in applying mainstream maximum likelihood inference upon extreme values is articulated on the scarcity of extreme observations for bringing the extreme value theorem to hold across a series of…
We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, that is, a density of the form $f_0=\exp\varphi_0$ where $\varphi_0$ is a concave function on $\mathbb{R}$. The pointwise…
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…
We study the smoothed log-concave maximum likelihood estimator of a probability distribution on $\mathbb{R}^d$. This is a fully automatic nonparametric density estimator, obtained as a canonical smoothing of the log-concave maximum…
In exploratory factor analysis, model parameters are usually estimated by maximum likelihood method. The maximum likelihood estimate is obtained by solving a complicated multivariate algebraic equation. Since the solution to the equation is…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…