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We define a Maximum Likelihood (ML for short) estimator for the correlation function, {\xi}, that uses the same pair counting observables (D, R, DD, DR, RR) as the standard Landy and Szalay (1993, LS for short) estimator. The ML estimator…
Motivated by studying asymptotic properties of the maximum likelihood estimator (MLE) in stochastic volatility (SV) models, in this paper we investigate likelihood estimation in state space models. We first prove, under some regularity…
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…
In recent years, Large Language Models (LLMs) have become fundamental to a broad spectrum of artificial intelligence applications. As the use of LLMs expands, precisely estimating the uncertainty in their predictions has become crucial.…
Every student in statistics or data science learns early on that when the sample size largely exceeds the number of variables, fitting a logistic model produces estimates that are approximately unbiased. Every student also learns that there…
We study semi-parametric estimation of the population mean when data is observed missing at random (MAR) in the $n < p$ "inconsistency regime", in which neither the outcome model nor the propensity/missingness model can be estimated…
Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We…
Joint maximum likelihood (JML) estimation is one of the earliest approaches to fitting item response theory (IRT) models. This procedure treats both the item and person parameters as unknown but fixed model parameters and estimates them…
Large Language Models (LLMs) tend to be unreliable in the factuality of their answers. To address this problem, NLP researchers have proposed a range of techniques to estimate LLM's confidence over facts. However, due to the lack of a…
Accurate uncertainty quantification (UQ) in Large Language Models (LLMs) is critical for trustworthy deployment. While real-world language is inherently ambiguous, reflecting aleatoric uncertainty, existing UQ methods are typically…
Prompt optimization algorithms for Large Language Models (LLMs) excel in multi-step reasoning but still lack effective uncertainty estimation. This paper introduces a benchmark dataset to evaluate uncertainty metrics, focusing on Answer,…
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with…
Indirect Inference (I-I) is a popular technique for estimating complex parametric models whose likelihood function is intractable, however, the statistical efficiency of I-I estimation is questionable. While the efficient method of moments,…
This study introduces the Misclassification Likelihood Matrix (MLM) as a novel tool for quantifying the reliability of neural network predictions under distribution shifts. The MLM is obtained by leveraging softmax outputs and clustering…
The maximum likelihood estimator (MLE) is pivotal in statistical inference, yet its application is often hindered by the absence of closed-form solutions for many models. This poses challenges in real-time computation scenarios,…
Walley's Imprecise Dirichlet Model (IDM) for categorical data overcomes several fundamental problems which other approaches to uncertainty suffer from. Yet, to be useful in practice, one needs efficient ways for computing the…
Neural language models (LMs) can be used to evaluate the truth of factual statements in two ways: they can be either queried for statement probabilities, or probed for internal representations of truthfulness. Past work has found that these…
Large language models are increasingly relied upon as sources of information, but their propensity for generating false or misleading statements with high confidence poses risks for users and society. In this paper, we confront the critical…
Rigorous statistical evaluations of large language models (LLMs), including valid error bars and significance testing, are essential for meaningful and reliable performance assessment. Currently, when such statistical measures are reported,…
This short note is to point the reader to notice that the proof of high dimensional asymptotic normality of MLE estimator for logistic regression under the regime $p_n=o(n)$ given in paper: "Maximum likelihood estimation in logistic…