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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…
The method of maximum likelihood estimation (MLE) is a widely used statistical approach for estimating the values of one or more unknown parameters of a probabilistic model based on observed data. In this tutorial, I briefly review the…
In this paper, different strands of literature are combined in order to obtain algorithms for semi-parametric estimation of discrete choice models that include the modelling of unobserved heterogeneity by using mixing distributions for the…
We use the delta method and Stein's method to derive, under regularity conditions, explicit upper bounds for the distributional distance between the distribution of the maximum likelihood estimator (MLE) of a $d$-dimensional parameter and…
Ideally, any statistical inference should be robust to local influences. Although there are simple ways to check about leverage points in independent and linear problems, more complex models require more sophisticated methods.…
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation produces a perturbation of sample data, which we call a…
Estimation of the mean and covariance parameters for functional data is a critical task, with local linear smoothing being a popular choice. In recent years, many scientific domains are producing multivariate functional data for which $p$,…
Fine-tuning LLMs on tabular classification tasks can lead to the phenomenon of fine-tuning multiplicity where equally well-performing models make conflicting predictions on the same input. Fine-tuning multiplicity can arise due to…
Latent space models have been widely adopted in modeling network data. Developing statistical inference for estimated model parameters enables quantifying associated uncertainty and is pivotal for downstream tasks. Despite recent progress…
This paper considers the nonparametric maximum likelihood estimator (MLE) for the joint distribution function of an interval censored survival time and a continuous mark variable. We provide a new explicit formula for the MLE in this…
Accurate and automated detection of anomalous samples in a natural image dataset can be accomplished with a probabilistic model for end-to-end modeling of images. Such images have heterogeneous complexity, however, and a probabilistic model…
Representing, comparing, and measuring the distance between probability distributions is a key task in computational statistics and machine learning. The choice of representation and the associated distance determine properties of the…
We propose a scalable divergence estimation method based on hashing. Consider two continuous random variables $X$ and $Y$ whose densities have bounded support. We consider a particular locality sensitive random hashing, and consider the…
This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…
We present local ensembles, a method for detecting underspecification -- when many possible predictors are consistent with the training data and model class -- at test time in a pre-trained model. Our method uses local second-order…
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…
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…
This paper is an attempt to set a justification for making use of some dicrepancy indexes, starting from the classical Maximum Likelihood definition, and adapting the corresponding basic principle of inference to situations where…
This work studies the properties of the maximum likelihood estimator (MLE) of a non-linear model with Gaussian errors and multidimensional parameter. The observations are collected in a two-stage experimental design and are dependent since…
Proper scoring rules evaluate the quality of probabilistic predictions, playing an essential role in the pursuit of accurate and well-calibrated models. Every proper score decomposes into two fundamental components -- proper calibration…