Related papers: Chi-square Fitting When Overall Normalization is a…
Exact expressions are given for the distribution function of the ratio of a weighted sum of independent chi-squared variables to a single chi-square variable, scaled appropriately. This distribution is the generalization of the classical F…
This paper develops several interesting, significant, and interconnected approaches to nonparametric or semi-parametric statistical inferences. The overwhelmingly favoured maximum likelihood estimator (MLE) under parametric model is…
In the analysis of count data often the equidispersion assumption is not suitable, hence the Poisson regression model is inappropriate. As a generalization of the Poisson distribution, the COM-Poisson distribution can deal with under-,…
Despite their advantages, normalizing flows generally suffer from several shortcomings including their tendency to generate unrealistic data (e.g., images) and their failing to detect out-of-distribution data. One reason for these…
Maximum likelihood estimation is a common method of estimating the parameters of the probability distribution from a given sample. This paper aims to introduce the maximum likelihood estimation in the framework of sublinear expectation. We…
We present a least squares method for estimating parameters from measurements of event yields in the presence of background and crossfeed. We adopt a unified approach to incorporating the statistical and systematic uncertainties on the…
Time-series anomaly detection deals with the problem of detecting anomalous timesteps by learning normality from the sequence of observations. However, the concept of normality evolves over time, leading to a "new normal problem", where the…
In this article we study the problem of recovering the unknown solution of a linear ill-posed problem, via iterative regularization methods. We review the problem of projection-regularization from a statistical point of view. A basic…
The contribution of this work is the introduction of a multivariate circular-linear (or poly- cylindrical) distribution obtained by combining the projected and the skew-normal. We show the flexibility of our proposal, its property of…
Although the likelihood function is normalizeable with respect to the data there is no guarantee that the same holds with respect to the model parameters. This may lead to singularities in the expectation value integral of these parameters,…
Particle physics experiments use likelihood ratio tests extensively to compare hypotheses and to construct confidence intervals. Often, the null distribution of the likelihood ratio test statistic is approximated by a $\chi^2$ distribution,…
Regularization is a popular technique to solve the overfitting problem of machine learning algorithms. Most regularization technique relies on parameter selection of the regularization coefficient. Plug-in method and cross-validation…
Least squares is by far the simplest and most commonly applied computational method in many fields. In almost all applications, the least squares objective is rarely the true objective. We account for this discrepancy by parametrizing the…
In the real world, experimental data are rarely, if ever, distributed as a normal (Gaussian) distribution. As an example, a large set of data--such as the cross sections for particle scattering as a function of energy contained in the…
This paper deals with the application of Approximation Theory type techniques to study a classical problem in Probability: estimating the parameter of a biased coin. For this purpose, a Minimax Estimation problem is considered and the…
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that…
Most extreme events in real life can be faithfully modeled as random realizations from a Generalized Pareto distribution, which depends on two parameters: the scale and the shape. In many actual situations, one is mostly concerned with the…
Chi-squared random fields arise naturally from the study of fluctuations in field theories with SO(n) symmetry. The extrema of chi-squared fields are of particular physical interest. In this paper, we undertake a statistical analysis of the…
We propose a simple test for moment inequalities that has exact size in normal models with known variance and has uniformly asymptotically exact size more generally. The test compares the quasi-likelihood ratio statistic to a chi-squared…
Many mathematical imaging problems are posed as non-convex optimization problems. When numerically tractable global optimization procedures are not available, one is often interested in testing ex post facto whether or not a locally…