Related papers: On the Phase Transition of Wilk's Phenomenon
Psychological disorders like major depressive disorder can be seen as complex dynamical systems. By looking at symptom activation patterns, we can investigate the dynamic behaviour of individuals to see whether or not they are at risk for…
The problem of testing the goodness of fit of an absolutely continuous distribution to a set of observations grouped into equal probability intervals, against to a family of sequences of alternatives approaching the hypothesis is…
In subgroup analysis, testing the existence of a subgroup with a differential treatment effect serves as protection against spurious subgroup discovery. Despite its importance, this hypothesis testing possesses a complicated nature:…
Testing hypothesis of independence between two random elements on a joint alphabet is a fundamental exercise in statistics. Pearson's chi-squared test is an effective test for such a situation when the contingency table is relatively small.…
We investigate the influence of chiral symmetry which varies along the space-time evolution of the system by considering the chiral phase transition in an non-equilibrium expanding quark-antiquark system. The chiral symmetry is described by…
It is well known that the approximate distribution of the usual test statistic of a goodness-of-fit test is chi-square, with degrees of freedom equal to the number of categories minus 1 (assuming that no parameters are to be estimated --…
Empirical likelihood enables a nonparametric, likelihood-driven style of inference without restrictive assumptions routinely made in parametric models. We develop a framework for applying empirical likelihood to the analysis of experimental…
We develop a jackknife empirical likelihood (JEL) framework for inference on parameters defined through multivariate three-sample U-statistic. From three independent multivariate samples, we construct JEL ratio statistic based on suitable…
We consider whether the asymptotic distributions for the log-likelihood ratio test statistic are expected to be Gaussian or chi-squared. Two straightforward examples provide insight on the difference.
Weighted histograms in Monte Carlo simulations are often used for the estimation of probability density functions. They are obtained as a result of random experiments with random events that have weights. In this paper, the bin contents of…
This short note considers the problem of testing the null hypothesis that the mean values of two multivariate normal variables are proportional. We show that the usual likelihood ratio $\chi^2$-test is valid non-asymptotically. Our proof…
Small sample sizes in clinical studies arises from factors such as reduced costs, limited subject availability, and the rarity of studied conditions. This creates challenges for accurately calculating confidence intervals (CIs) using the…
Pearson's Chi-square test is a widely used tool for analyzing categorical data, yet its statistical power has remained theoretically underexplored. Due to the difficulties in obtaining its power function in the usual manner, Cochran (1952)…
Multiparametric statistical model providing stable reconstruction of parameters by observations is considered. The only general method of this kind is the root model based on the representation of the probability density as a squared…
This paper revisits the classical inference results for profile quasi maximum likelihood estimators (profile MLE) in the semiparametric estimation problem. We mainly focus on two prominent theorems: the Wilks phenomenon and Fisher expansion…
"Asymptotic formulae for likelihood-based tests of new physics" presents a mathematical formalism for a new approximation for hypothesis testing in high energy physics. The approximations are designed to greatly reduce the computational…
The 'standard' confidence interval for a Poisson parameter is only one of a number of estimation intervals based on the chi-square distribution that may be used in the estimation of the mean or mean rate for a Poisson model. Other…
Phase transitions occupy a central role in physics, due both to their experimental ubiquity and their fundamental conceptual importance. The explanation of universality at phase transitions was the great success of the theory formulated by…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
The question of testing for equality in distribution between two linear models, each consisting of sums of distinct discrete independent random variables with unequal numbers of observations, has emerged from the biological research. In…