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In many statistical applications that concern mathematical psychologists, the concept of Fisher information plays an important role. In this tutorial we clarify the concept of Fisher information as it manifests itself across three different…
We study the empirical likelihood approach to construct confidence intervals for the optimal value and the optimality gap of a given solution, henceforth quantify the statistical uncertainty of sample average approximation, for optimization…
Profile likelihood confidence intervals are a robust alternative to Wald's method if the asymptotic properties of the maximum likelihood estimator are not met. However, the constrained optimization problem defining profile likelihood…
We investigate a Poisson sampling design in the presence of unknown selection probabilities when applied to a population of unknown size for multiple sampling occasions. The fixed-population model is adopted and extended upon for inference.…
Inference is the process of using facts we know to learn about facts we do not know. A theory of inference gives assumptions necessary to get from the former to the latter, along with a definition for and summary of the resulting…
Measures of uncertainty and divergence are introduced for interval-valued probability distributions and are shown to have desirable mathematical properties. A maximum uncertainty inference procedure for marginal interval distributions is…
Accurate simulation of complex physical systems enables the development, testing, and certification of control strategies before they are deployed into the real systems. As simulators become more advanced, the analytical tractability of the…
Approximate Bayesian computing is a powerful likelihood-free method that has grown increasingly popular since early applications in population genetics. However, complications arise in the theoretical justification for Bayesian inference…
The subjects of the paper are the likelihood method (LM) and the expected Fisher information (FI) considered from the point od view of the construction of the physical models which originate in the statistical description of phenomena. The…
Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to…
The incorporation of systematic uncertainties into confidence interval calculations has been addressed recently in a paper by Conrad et al. (Physical Review D 67 (2003) 012002). In their work, systematic uncertainities in detector…
Empirical likelihood is a popular nonparametric or semi-parametric statistical method with many nice statistical properties. Yet when the sample size is small, or the dimension of the accompanying estimating function is high, the…
Empirical likelihood is a well-known nonparametric method in statistics and has been widely applied in statistical inference. The method has been employed by Lu and Peng (2002) to constructing confidence intervals for the tail index of a…
Uncertainty quantification for estimation through stochastic optimization solutions in an online setting has gained popularity recently. This paper introduces a novel inference method focused on constructing confidence intervals with…
The authors propose a robust semi-parametric empirical likelihood method to integrate all available information from multiple samples with a common center of measurements. Two different sets of estimating equations are used to improve the…
We developed a statistical inference method applicable to a broad range of generalized linear models (GLMs) in high-dimensional settings, where the number of unknown coefficients scales proportionally with the sample size. Although a…
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a…
The purpose of this paper is to propose methodologies for statistical inference of low-dimensional parameters with high-dimensional data. We focus on constructing confidence intervals for individual coefficients and linear combinations of…
Firth-type logistic regression has become a standard approach for the analysis of binary outcomes with small samples. Whereas it reduces the bias in maximum likelihood estimates of coefficients, bias towards 1/2 is introduced in the…
The Birnbaum-Saunders distribution, also known as the fatigue-life distribution, is frequently used in reliability studies. We obtain adjustments to the Birnbaum--Saunders profile likelihood function. The modified versions of the likelihood…