相关论文: BEAUTY Powered BEAST
Based on $m$-fold integrated empirical measures, we study three new classes of goodness-of-fits tests, generalizing Anderson-Darling, Cram\'er-von Mises, and Watson statistics, respectively, and examine the corresponding limiting stochastic…
We develop a new statistical procedure to test whether the dependence structure is identical between two groups. Rather than relying on a single index such as Pearson's correlation coefficient or Kendall's Tau, we consider the entire…
Performance measurement is an essential task once a statistical model is created. The Area Under the receiving operating characteristics Curve (AUC) is the most popular measure for evaluating the quality of a binary classifier. In this…
In this paper new two-dimensional goodness of fit tests are proposed. They are of supremum-type and are based on different types of characterizations. For the first time a characterization based on independence of two statistics is used for…
A large class of goodness-of-fit test statistics based on sup-functionals of weighted empirical processes is proposed and studied. The weight functions employed are Erd\H{o}s-Feller-Kolmogorov-Petrovski upper-class functions of a Brownian…
We study best-of-$N$ for large language models (LLMs) where the selection is based on majority voting. In particular, we analyze the limit $N \to \infty$, which we denote as \boinflower. While this approach achieves impressive performance…
An evolutionary search space can be smoothly transformed via a suitable change of basis; however, it can be difficult to determine an appropriate basis. In this paper, a method is proposed to select an optimum basis can be used to simplify…
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 --…
When data analysts train a classifier and check if its accuracy is significantly different from chance, they are implicitly performing a two-sample test. We investigate the statistical properties of this flexible approach in the…
Kuiper's $V_n$ statistic, a measure for comparing the difference of ideal distribution and empirical distribution, is of great significance in the goodness-of-fit test. However, Kuiper's formulae for computing the cumulative distribution…
Equivalence testing, a fundamental problem in the field of distribution testing, seeks to infer if two unknown distributions on $[n]$ are the same or far apart in the total variation distance. Conditional sampling has emerged as a powerful…
In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient…
Assessing goodness of fit to a given distribution plays an important role in computational statistics. The Probability integral transformation (PIT) can be used to convert the question of whether a given sample originates from a reference…
In many applications, we encounter data on Riemannian manifolds such as torus and rotation groups. Standard statistical procedures for multivariate data are not applicable to such data. In this study, we develop goodness-of-fit testing and…
The field of causal discovery develops model selection methods to infer cause-effect relations among a set of random variables. For this purpose, different modelling assumptions have been proposed to render cause-effect relations…
The model-X conditional randomization test is a generic framework for conditional independence testing, unlocking new possibilities to discover features that are conditionally associated with a response of interest while controlling type-I…
We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…
We present a novel data-oriented statistical framework that assesses the presumed Gaussian dependence structure in a pairwise setting. This refers to both multivariate normality and normal copula goodness-of-fit testing. The proposed test…
A new and promising avenue was recently developed for analyzing large-scale structure data with a model-independent approach, in which the linear power spectrum shape is parametrized with a large number of freely varying wavebands rather…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…