Related papers: Maximum likelihood estimation in the sparse Rasch …
A central issue of many statistical learning problems is to select an appropriate model from a set of candidate models. Large models tend to inflate the variance (or overfitting), while small models tend to cause biases (or underfitting)…
Targeted maximum likelihood estimation is a general methodology combining flexible ensemble learning and semiparametric efficiency theory in a two-step procedure for estimation of causal parameters. Proposed targeted maximum likelihood…
This paper considers an extension of the multivariate symmetric Laplace distribution to matrix variate case. The symmetric Laplace distribution is a scale mixture of normal distribution. The maximum likelihood estimators (MLE) of the…
This paper introduces a unified framework for the detection of a source with a sensor array in the context where the noise variance and the channel between the source and the sensors are unknown at the receiver. The Generalized Maximum…
Bogdan et al. established a new criterion to determine the existence of a maximum likelihood estimator in discrete exponential families. It uses the notion of the set of uniqueness, which allows to apply the problem to the Ising model from…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
We revisit the problem of mean estimation in the Gaussian sequence model with $\ell_p$ constraints for $p \in [0, \infty]$. We demonstrate two phenomena for the behavior of the maximum likelihood estimator (MLE), which depend on the noise…
Abundance estimation from capture-recapture data is of great importance in many disciplines. Analysis of capture-recapture data is often complicated by the existence of one-inflation and heterogeneity problems. Simultaneously taking these…
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…
Frequently one has to search within a finite population for a single particular individual or item with a rare characteristic. Whether an item possesses the characteristic can only be determined by close inspection. The availability of…
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…
We propose a general approach to construct weighted likelihood estimating equations with the aim of obtaining robust parameter estimates. We modify the standard likelihood equations by incorporating a weight that reflects the statistical…
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 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…
Given a large number of covariates $Z$, we consider the estimation of a high-dimensional parameter $\theta$ in an individualized linear threshold $\theta^T Z$ for a continuous variable $X$, which minimizes the disagreement between…
This paper considers the maximum likelihood estimation of factor models of high dimension, where the number of variables (N) is comparable with or even greater than the number of observations (T). An inferential theory is developed. We…
Recommendations based on behavioral data may be faced with ambiguous statistical evidence. We consider the case of association rules, relevant e.g.~for query and product recommendations. For example: Suppose that a customer belongs to…
Online planning in Markov Decision Processes (MDPs) enables agents to make sequential decisions by simulating future trajectories from the current state, making it well-suited for large-scale or dynamic environments. Sample-based methods…
New experimental methods make it possible to measure the expression levels of many genes, simultaneously, in snapshots from thousands or even millions of individual cells. Current approaches to analyze these experiments involve clustering…