Related papers: A Closed Form Maximum Likelihood Estimator to End-…

For a multinomial distribution, suppose that we have prior knowledge of the sum of the probabilities of some categories. This allows us to construct a submodel in a full (i.e., no-restriction) model. Maximum likelihood estimation (MLE)…

The problem of reducing the bias of maximum likelihood estimator in a general multivariate elliptical regression model is considered. The model is very flexible and allows the mean vector and the dispersion matrix to have parameters in…

Providing theoretical guarantees for parameter estimation in exponential random graph models is a largely open problem. While maximum likelihood estimation has theoretical guarantees in principle, verifying the assumptions for these…

Spectral learning recently generated lots of excitement in machine learning, largely because it is the first known method to produce consistent estimates (under suitable conditions) for several latent variable models. In contrast, maximum…

We show that the maximum likelihood estimator (MLE) is an effective tool for mitigating non-flow effects in flow analysis. To this end, one constructs two toy models that simulate non-flow contributions corresponding to particle decay and…

Estimators derived from a divergence criterion such as $\varphi-$divergences are generally more robust than the maximum likelihood ones. We are interested in particular in the so-called MD$\varphi$DE, an estimator built using a dual…

We propose a new method for multivariate response regression and covariance estimation when elements of the response vector are of mixed types, for example some continuous and some discrete. Our method is based on a model which assumes the…

In a multi-fidelity setting, data are available from two sources, high- and low-fidelity. Low-fidelity data has larger size and can be leveraged to make more efficient inference about quantities of interest, e.g. the mean, for high-fidelity…

In a typical two-phase design, a random sample is drawn from the target population in phase 1, during which only a subset of variables is collected. In phase 2, a subsample of the phase-1 cohort is selected, and additional variables are…

Let $x_{i,j}$, $1 \le i \le m$, $1 \le j \le n_i$, be observations from a doubly-indexed sequence $\{X_{i,j}\}$ of independent random variables (all of them discrete, or all of them absolutely continuous). Suppose that each $X_{i,j}$ has…

We propose and study a maximum likelihood estimator of stochastic frontier models with endogeneity in cross-section data when the composite error term may be correlated with inputs and environmental variables. Our framework is a…

Mixtures of factor analyzers are becoming more and more popular in the area of model based clustering of high-dimensional data. According to the likelihood approach in data modeling, it is well known that the unconstrained log-likelihood…

We find upper bounds for the probability of underestimation and overestimation errors in penalized likelihood context tree estimation. The bounds are explicit and applies to processes of not necessarily finite memory. We allow for general…

Mixture distributions with dynamic weights are an efficient way of modeling loss data characterized by heavy tails. However, maximum likelihood estimation of this family of models is difficult, mostly because of the need to evaluate…

In this report, we explore the data selection leading to a family of estimators maximizing a centrality. The family allows a nice properties leading to accurate and robust probability density function fitting according to some criteria we…

This paper introduces a new biased estimator for the negative binomial regression model that is a generalization of Liu-type estimator proposed for the linear model in [12]. Since the variance of the maximum likelihood estimator (MLE) is…

The ability to rigorously estimate the failure rates of large language models (LLMs) is a prerequisite for their safe deployment. Currently, however, practitioners often face a tradeoff between expensive human gold standards and potentially…

We study three fundamental statistical-learning problems: distribution estimation, property estimation, and property testing. We establish the profile maximum likelihood (PML) estimator as the first unified sample-optimal approach to a wide…

We study the problem of maximum likelihood (ML) estimation for statistical models defined by reflexive polytopes. Our focus is on the maximum likelihood degree of these models as an algebraic measure of complexity of the corresponding…

In this paper, we study the linear transformation model in the most general setup. This model includes many important and popular models in statistics and econometrics as special cases. Although it has been studied for many years, the…