Related papers: Gaussian Universal Likelihood Ratio Testing
In this work, we provide a refinement of the selective CLT result of Tian and Taylor (2015), which allows for selective inference in non-parametric settings by adjusting for the asymptotic Gaussian limit for selection. Under some regularity…
The Gaussian graphical model is routinely employed to model the joint distribution of multiple random variables. The graph it induces is not only useful for describing the relationship between random variables but also critical for…
Relational data are often represented as a square matrix, the entries of which record the relationships between pairs of objects. Many statistical methods for the analysis of such data assume some degree of similarity or dependence between…
The classic chi-squared statistic for testing goodness-of-fit has long been a cornerstone of modern statistical practice. The statistic consists of a sum in which each summand involves division by the probability associated with the…
Traditional meta-analysis assumes that the effect sizes estimated in individual studies follow a Gaussian distribution. However, this distributional assumption is not always satisfied in practice, leading to potentially biased results. In…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
A very simple Gaussian model is used to illustrate a new fitting result: a linear growth of the resolution with the number N of detecting layers. This rule is well beyond the well-known rule proportional to $\sqrt{N}$ for the resolution of…
We propose the so-called jackknife empirical likelihood approach for the survey data of general unequal probability sampling designs, and analyze parameters defined according to U-statistics. We prove theoretically that jackknife…
Nonparametric tests for equality of multivariate distributions are frequently desired in research. It is commonly required that test-procedures based on relatively small samples of vectors accurately control the corresponding Type I Error…
This study develops a framework for testing hypotheses on structural parameters in incomplete models. Such models make set-valued predictions and hence do not generally yield a unique likelihood function. The model structure, however,…
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.…
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,…
Random matrix theory (RMT) successfully predicts universal statistical properties of complicated wave scattering systems in the semiclassical limit, while the random coupling model offers a complete statistical model with a simple additive…
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 generalized likelihood ratio (GLR) test proposed by Fan, Zhang and Zhang [Ann. Statist. 29 (2001) 153-193] and Fan and Yao [Nonlinear Time Series: Nonparametric and Parametric Methods (2003) Springer] is a generally applicable…
We study two-sample equality testing in Gaussian graphical models. Classical likelihood ratio tests on decomposable graphs admit clique-wise factorizations, offering limited localization and unstable finite-sample behaviour. We propose…
In this paper, we revisit the classical goodness-of-fit problems for univariate distributions; we propose a new testing procedure based on a characterisation of the uniform distribution. Asymptotic theory for the simple hypothesis case is…
In this paper, we develop a generalization of the Gaussian quasi score test (GQST) for composite binary hypothesis testing. The proposed test, called measure transformed GQST (MT-GQST), is based on the score-function of the measure…
In the statistical inference for long range dependent time series the shape of the limit distribution typically depends on unknown parameters. Therefore, we propose to use subsampling. We show the validity of subsampling for general…
As technology continues to advance at a rapid pace, the prevalence of multivariate functional data (MFD) has expanded across diverse disciplines, spanning biology, climatology, finance, and numerous other fields of study. Although MFD are…