Related papers: Point estimation with exponentially tilted empiric…
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…
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…
The problem of nonlinear functional of parameters, such as differential entropy, has received much attention in information theory and statistics. In many situations, prior information about the parameters is available in the form of order…
Asymptotic efficiency of targeted maximum likelihood estimators (TMLE) of target features of the data distribution relies on a a second order remainder being asymptotically negligible. In previous work we proposed a nonparametric MLE termed…
Generalized linear mixed models are powerful tools for analyzing clustered data, where the unknown parameters are classically (and most commonly) estimated by the maximum likelihood and restricted maximum likelihood procedures. However,…
Pattern learning in an important problem in Natural Language Processing (NLP). Some exhaustive pattern learning (EPL) methods (Bod, 1992) were proved to be flawed (Johnson, 2002), while similar algorithms (Och and Ney, 2004) showed great…
The minimum error entropy (MEE) criterion has been successfully used in fields such as parameter estimation, system identification and the supervised machine learning. There is in general no explicit expression for the optimal MEE estimate…
We study a class of weakly identifiable location-scale mixture models for which the maximum likelihood estimates based on $n$ i.i.d. samples are known to have lower accuracy than the classical $n^{- \frac{1}{2}}$ error. We investigate…
We develop a general framework for proving rigorous guarantees on the performance of the EM algorithm and a variant known as gradient EM. Our analysis is divided into two parts: a treatment of these algorithms at the population level (in…
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…
We propose an $\ell_1$-penalized estimator for high-dimensional models of Expected Shortfall (ES). The estimator is obtained as the solution to a least-squares problem for an auxiliary dependent variable, which is defined as a…
Many statistical estimators are defined as the fixed point of a data-dependent operator, with estimators based on minimizing a cost function being an important special case. The limiting performance of such estimators depends on the…
We study maximum likelihood estimation in log-linear models under conditional Poisson sampling schemes. We derive necessary and sufficient conditions for existence of the maximum likelihood estimator (MLE) of the model parameters and…
In the mean field (or random link) model there are $n$ points and inter-point distances are independent random variables. For $0 < \ell < \infty$ and in the $n \to \infty$ limit, let $\delta(\ell) = 1/n \times$ (maximum number of steps in a…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
Reliable precipitation nowcasting is critical for weather-sensitive decision-making, yet neural weather models (NWMs) can produce poorly calibrated probabilistic forecasts. Standard calibration metrics such as the expected calibration error…
We consider 1-dimensional location estimation, where we estimate a parameter $\lambda$ from $n$ samples $\lambda + \eta_i$, with each $\eta_i$ drawn i.i.d. from a known distribution $f$. For fixed $f$ the maximum-likelihood estimate (MLE)…
The main aim of this article is to characterize and investigate the three parameter exponentiated exponential Poisson probability distribution ${\rm EEP}(\alpha, \beta, \lambda)$ by giving explicit closed form expressions for its…
The change-plane Cox model is a popular tool for the subgroup analysis of survival data. Despite the rich literature on this model, there has been limited investigation into the asymptotic properties of the estimators of the…
Causal inference problems have remained an important research topic over the past several decades due to their general applicability in assessing a treatment effect in many different real-world settings. In this paper, we propose two…