Related papers: Generalized maximum likelihood estimation of the m…
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…
Maximum likelihood is the most widely used statistical estimation technique. Recent work by the authors introduced a general methodology for the construction of estimators for functionals in parametric models, and demonstrated improvements…
Empirical Bayes methods are widely used for large-scale estimation and inference in the Poisson means problem. Existing results establish theoretical properties of the nonparametric maximum likelihood estimator (NPMLE) for optimal posterior…
We advocate for a practical Maximum Likelihood Estimation (MLE) approach towards designing loss functions for regression and forecasting, as an alternative to the typical approach of direct empirical risk minimization on a specific target…
In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal…
We study a parametric estimation problem related to moment condition models. As an alternative to the generalized empirical likelihood (GEL) and the generalized method of moments (GMM), a Bayesian approach to the problem can be adopted,…
This undergraduate thesis focuses on calculating maximum likelihood estimates of parameters in the generalized Gamma distribution using the SeLF algorithm. As an extension of the Gamma distribution, the generalized Gamma distribution can…
We study modeling and inference with the Elliptical Gamma Distribution (EGD). We consider maximum likelihood (ML) estimation for EGD scatter matrices, a task for which we develop new fixed-point algorithms. Our algorithms are efficient and…
For many applications, an ensemble of base classifiers is an effective solution. The tuning of its parameters(number of classes, amount of data on which each classifier is to be trained on, etc.) requires G, the generalization error of a…
Principal stratification is a widely used framework for addressing post-randomization complications. After using principal stratification to define causal effects of interest, researchers are increasingly turning to finite mixture models to…
We study the asymptotic properties of parameter estimation and predictive inference under the exchangeable Gibbs partition, characterized by a discount parameter $\alpha\in(0,1)$ and a triangular array $v_{n,k}$ satisfying a backward…
Towards understanding the fundamental limits of estimation from data of varied quality, we study the problem of estimating a mean parameter from heteroskedastic Gaussian observations where the variances are unknown and may vary arbitrarily…
Understanding the processes that influence groundwater levels is crucial for forecasting and responding to hazards such as groundwater droughts. Mixed models, which combine a fixed mean, expressed using independent predictors, with…
The four-parameter kappa distribution (K4D) is a generalized form of some commonly used distributions such as generalized logistic, generalized Pareto, generalized Gumbel, and generalized extreme value (GEV) distributions. Owing to its…
We consider distributed estimation of the inverse covariance matrix, also called the concentration or precision matrix, in Gaussian graphical models. Traditional centralized estimation often requires global inference of the covariance…
We consider the problem of estimating a mixture of power series distributions with infinite support, to which belong very well-known models such as Poisson, Geometric, Logarithmic or Negative Binomial probability mass functions. We consider…
In this article, we revisit the problem of fitting a mixture model under the assumption that the mixture components are symmetric and log-concave. To this end, we first study the nonparametric maximum likelihood estimation (NPMLE) of a…
Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling…
The method of generalized estimating equations (GEE) is popular in the biostatistics literature for analyzing longitudinal binary and count data. It assumes a generalized linear model (GLM) for the outcome variable, and a working…
This paper derives the nonparametric maximum likelihood estimator (NPMLE) of a distribution function from observations which are subject to both bias and censoring. The NPMLE is obtained by a simple EM algorithm which is an extension of the…