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We propose a family of tests to assess the goodness-of-fit of a high-dimensional generalized linear model. Our framework is flexible and may be used to construct an omnibus test or directed against testing specific non-linearities and…
In astronomy, we frequently face the decision problem: does this data contain a signal? Typically, a statistical approach is used, which requires a threshold. The choice of threshold presents a common challenge in settings where signals and…
Consistent experiment data are crucial to adjust parameters of physics models and to determine best estimates of observables. However, often experiment data are not consistent due to unrecognized systematic errors. Standard methods of…
Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…
This paper considers the problem of cardinality estimation in data stream applications. We present a statistical analysis of probabilistic counting algorithms, focusing on two techniques that use pseudo-random variates to form…
In recent years, many non-traditional classification methods, such as Random Forest, Boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the…
This paper develops a smooth test of goodness-of-fit for elliptical distributions. The test is adaptively omnibus, invariant to affine-linear transformations and has a convenient expression that can be broken into components. These…
We present improved methods for calculating confidence intervals and $p$-values in situations where standard asymptotic approaches fail due to small sample sizes. We apply these techniques to a specific class of statistical model that can…
We describe a test statistic for unbinned goodness-of-fit of data in one dimension. The statistic is based on the two-dimensional Random Walk. The rejection power of this test is explored both for simple and compound hypotheses and, for the…
We consider the problem of the construction of the Goodness-of-Fit test in the case of continuous time observations of a diffusion process with small noise. The null hypothesis is parametric and we use a minimum distance estimator of the…
The problem of assessing a parametric regression model in the presence of spatial correlation is addressed in this work. For that purpose, a goodness-of-fit test based on a $L_2$-distance comparing a parametric and a nonparametric…
In population genetics and other application fields, models with intractable likelihood are common. Approximate Bayesian Computation (ABC) or more generally Simulation-Based Inference (SBI) methods work by simulating instrumental data sets…
We construct integral and supremum type goodness-of-fit tests for the family of power distribution functions. Test statistics are functionals of $U-$empirical processes and are based on the classical characterization of power function…
Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit…
A Gaussianity analysis using a goodness-of-fit test and the Minkowski functionals on the sphere has been performed to study the measured Archeops Cosmic Microwave Background (CMB) temperature anisotropy data for a 143 GHz Archeops…
This paper introduces diagnostic tests for the nature of lack of fit in ordinary differential equation models (ODEs) proposed for data. We present a hierarchy of three possible sources of lack of fit: unaccounted-for stochastic variation,…
The likelihood ratio statistic, with its asymptotic $\chi^2$ distribution at regular model points, is often used for hypothesis testing. At model singularities and boundaries, however, the asymptotic distribution may not be $\chi^2$, as…
We study statistics dependence of the probability distributions and the means of measured moments of conserved quantities, respectively. The required statistics of all interested moments and their products are estimated based on a simple…
In this paper we introduce a novel statistical framework based on the first two quantile conditional moments that facilitates effective goodness-of-fit testing for one-sided L\'evy distributions. The scale-ratio framework introduced in this…
We present the results of a large number of simulation studies regarding the power of various goodness-of-fit as well as nonparametric two-sample tests for univariate data. This includes both continuous and discrete data. In general no…