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Related papers: A Robust Test for Elliptical Symmetry

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We consider robust covariance estimation with group symmetry constraints. Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and Multivariate Generalized Gaussian distribution methods, usually involve non-convex minimization…

Machine Learning · Statistics 2013-06-19 Ilya Soloveychik , Ami Wiesel

The accurate specification of the number of factors is critical to the validity of factor models and the topic almost occupies the central position in factor analysis. Plenty of estimators are available under the restrictive condition that…

Methodology · Statistics 2019-08-15 Long Yu , Yong He , Xinsheng Zhang

Recently there have been many research efforts in developing generative models for self-exciting point processes, partly due to their broad applicability for real-world applications. However, rarely can we quantify how well the generative…

Statistics Theory · Mathematics 2021-02-15 Song Wei , Shixiang Zhu , Minghe Zhang , Yao Xie

The Functional Linear Model with Functional Response (FLMFR) is one of the most fundamental models to assess the relation between two functional random variables. In this paper, we propose a novel goodness-of-fit test for the FLMFR against…

We revisit the Kolmogorov-Smirnov and Cram\'er-von Mises goodness-of-fit (GoF) tests and propose a generalisation to identically distributed, but dependent univariate random variables. We show that the dependence leads to a reduction of the…

Statistical Finance · Quantitative Finance 2011-09-06 Remy Chicheportiche , Jean-Philippe Bouchaud

Exact null distributions of goodness-of-fit test statistics are generally challenging to obtain in tractable forms. Practitioners are therefore usually obliged to rely on asymptotic null distributions or Monte Carlo methods, either in the…

Methodology · Statistics 2023-09-06 Alberto Fernández-de-Marcos , Eduardo García-Portugués

We develop tests for high-dimensional covariance matrices under a generalized elliptical model. Our tests are based on a central limit theorem (CLT) for linear spectral statistics of the sample covariance matrix based on self-normalized…

Statistics Theory · Mathematics 2019-12-17 Xinxin Yang , Xinghua Zheng , Jiaqi Chen

In this work, the distributional properties of the goodness-of-fit term in likelihood-based information criteria are explored. These properties are then leveraged to construct a novel goodness-of-fit test for normal linear regression models…

Methodology · Statistics 2023-09-20 Scott H. Koeneman , Joseph E. Cavanaugh

We propose a new asymptotic test for the separability of a covariance matrix. The null distribution is valid in wide matrix elliptical model that includes, in particular, both matrix Gaussian and matrix $t$-distribution. The test is fast to…

Statistics Theory · Mathematics 2026-01-26 Joni Virta , Takeru Matsuda

A natural (yet unconventional) test for goodness-of-fit measures the discrepancy between the model and empirical distributions via their Euclidean distance (or, equivalently, via its square). The present paper characterizes the statistical…

Computation · Statistics 2012-06-28 William Perkins , Gary Simon , Mark Tygert

Over the past decades, there has been a surge of interest in studying low-dimensional structures within high-dimensional data. Statistical factor models $-$ i.e., low-rank plus diagonal covariance structures $-$ offer a powerful framework…

Machine Learning · Statistics 2025-05-20 Daniel Cederberg

We introduce a new statistical test based on the observed spacings of ordered data. The statistic is sensitive to detect non-uniformity in random samples, or short-lived features in event time series. Under some conditions, this new test…

Methodology · Statistics 2022-10-27 Philipp Eller , Lolian Shtembari

We introduce the \textit{almost goodness-of-fit} test, a procedure to assess whether a (parametric) model provides a good representation of the probability distribution generating the observed sample. Specifically, given a distribution…

Methodology · Statistics 2025-10-15 Amparo Baíllo , Javier Cárcamo

The proposed Goodness--of--Fit (GoF) test for checking the linear autocorrelation model in a functional time series is based on an empirical process, whose residual marks and covariate index set are in a separable Hilbert space \mathbb{H}.…

Statistics Theory · Mathematics 2026-05-29 W. González-Manteiga , M. D. Ruiz-Medina , M. Febrero-Bande

The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively…

Methodology · Statistics 2012-10-08 Ivan Kojadinovic , Jun Yan

We study the problem of robustly estimating the mean or location parameter without moment assumptions. We show that for a large class of symmetric distributions, the same error as in the Gaussian setting can be achieved efficiently. The…

Data Structures and Algorithms · Computer Science 2023-11-09 Gleb Novikov , David Steurer , Stefan Tiegel

Mixture modelling using elliptical distributions promises enhanced robustness, flexibility and stability over the widely employed Gaussian mixture model (GMM). However, existing studies based on the elliptical mixture model (EMM) are…

Machine Learning · Computer Science 2020-09-30 Shengxi Li , Zeyang Yu , Danilo Mandic

Multivariate elliptically-contoured distributions are widely used for modeling correlated and non-Gaussian data. In this work, we study the kurtosis of the elliptical model, which is an important parameter in many statistical analysis.…

Statistics Theory · Mathematics 2024-08-23 Bowen Zhou , Peirong Xu , Cheng Wang

Spaces with locally varying scale of measurement, like multidimensional structures with differently scaled dimensions, are pretty common in statistics and machine learning. Nevertheless, it is still understood as an open question how to…

Machine Learning · Statistics 2024-03-05 Christoph Jansen , Georg Schollmeyer , Hannah Blocher , Julian Rodemann , Thomas Augustin

Goodness-of-fit (GoF) tests are a fundamental component of statistical practice, essential for checking model assumptions and testing scientific hypotheses. Despite their widespread use, popular GoF tests exhibit surprisingly low…

Methodology · Statistics 2025-10-28 Christian T. Covington , Jeffrey W. Miller