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The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…

We consider an empirical likelihood framework for inference for a statistical model based on an informative sampling design. Covariate information is incorporated both through the weights and the estimating equations. The estimator is based…

We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling…

Models defined by moment conditions are at the center of structural econometric estimation, but economic theory is mostly agnostic about moment selection. While a large pool of valid moments can potentially improve estimation efficiency, in…

Time- and state-domain methods are two common approaches for nonparametric prediction. The former predominantly uses the data in the recent history while the latter mainly relies on historical information. The question of combining these…

Likelihood-free inference (LFI) has been successfully applied to state-space models, where the likelihood of observations is not available but synthetic observations generated by a black-box simulator can be used for inference instead.…

In this paper, the authors first provide an overview of two major developments on complex survey data analysis: the empirical likelihood methods and statistical inference with non-probability survey samples, and highlight the important…

Estimator selection has become a crucial issue in non parametric estimation. Two widely used methods are penalized empirical risk minimization (such as penalized log-likelihood estimation) or pairwise comparison (such as Lepski's method).…

When an expert operates a perilous dynamic system, ideal constraint information is tacitly contained in their demonstrated trajectories and controls. The likelihood of these demonstrations can be computed, given the system dynamics and task…

Insurance loss data are usually in the form of left-truncation and right-censoring due to deductibles and policy limits respectively. This paper investigates the model uncertainty and selection procedure when various parametric models are…

Estimation methods for the L\'{e}vy density of a L\'{e}vy process are developed under mild qualitative assumptions. A classical model selection approach made up of two steps is studied. The first step consists in the selection of a good…

One of the most important problems in system identification and statistics is how to estimate the unknown parameters of a given model. Optimization methods and specialized procedures, such as Empirical Minimization (EM) can be used in case…

In this paper we address the challenging problem of designing globally convergent estimators for the parameters of nonlinear systems containing a non-separable exponential nonlinearity. This class of terms appears in many practical…

In this work we consider the unbiased estimation of expectations w.r.t.~probability measures that have non-negative Lebesgue density, and which are known point-wise up-to a normalizing constant. We focus upon developing an unbiased method…

For model-based estimation methods, the modeling that is as close to reality as possible makes a vital estimation result. In simple applications, it is sufficient to model a system with a single state space model. However, there are…

I consider two problems in machine learning and statistics: the problem of estimating the joint probability density of a collection of random variables, known as density estimation, and the problem of inferring model parameters when their…

Accurately quantifying uncertainty in large language models (LLMs) is crucial for their reliable deployment, especially in high-stakes applications. Current state-of-the-art methods for measuring semantic uncertainty in LLMs rely on strict…

Applications of structural equation models (SEMs) are often restricted to linear associations between variables. Maximum likelihood (ML) estimation in non-linear models may be complex and require numerical integration. Furthermore, ML…

Simulation-based inference enables learning the parameters of a model even when its likelihood cannot be computed in practice. One class of methods uses data simulated with different parameters to infer models of the likelihood-to-evidence…