arXiv subjects

Sophia Loizidou

Publications and source records attributed to Sophia Loizidou.

6 recordsLinked to original sources

arXiv2026

Construction of optimal tests for symmetry on the torus and their quantitative error bounds

In this paper, we investigate the general problem of assessing symmetry in data points on the hyper-dimensional torus, a question that originally emerged in applications from bioinformatics and directional statistics. We develop optimal tests for symmetry for both scenarios where the center of symmetry is known and where it is unknown. Our new tests are not only valid under a given parametric hypothesis but also under a very broad class of symmetric distributions. The asymptotic behavior of the proposed tests is studied both under the null hypothesis and local alternatives. A key contribution of our paper is that we accompany our asymptotic results with error guarantees by deriving quantitative bounds on the distributional distance between the exact (unknown) distribution of the test statistic and its asymptotic counterpart by leveraging Stein's method. The finite-sample performance of the tests is evaluated through simulation studies, and their practical utility in bioinformatics is demonstrated via an application to protein folding data.

math.ST↗

arXiv2026

Multiple change-point detection on the circle via isolation using permutation testing

In this paper we propose a new method for multiple change-point detection for piecewise-constant circular signals, a setting that, despite its importance in many scientific domains, remains comparatively under-explored. The proposed method, Permutation-based Circular Isolate-Detect, denoted PCID, uses an appropriately chosen contrast function and permutation testing to detect change-points in an offline manner, for the data sequence under consideration. Prior to detection, PCID isolates the change-points. The contrast function used is derived under the assumption of von Mises distribution for the noise, but we show that the method is robust and performs well for other distributions as well. Simulations are used to showcase the usability of the method in different signal and noise structures, including serially correlated noise. In order to exhibit the practical relevance of the method in real-world applications, PCID is applied to three real-world datasets, namely flare, acrophase and wave data.

stat.ME↗

arXiv2026

On the singularity of the Fisher Information matrix in the sine-skewed family on the d-dimensional torus

Skewed distributions are fundamental in modelling asymmetric data on the d-dimensional torus. In this context, asymmetry is introduced through the sine-skewing mechanism, which is the only skewing mechanism that has been proposed on the hyper-torus in the literature. Some sine-skewed models are known to suffer from a singular Fisher information matrix in the vicinity of symmetry, which poses a significant issue for inferential purposes. It is an open question to determine for which sine-skewed models Fisher information singularity occurs. In this paper, a general characterization of the class of models that exhibit this singularity is given in the general d-dimensional setting.

math.ST↗

arXiv2025

Modelling toroidal and cylindrical data via the trivariate wrapped Cauchy copula with non-uniform marginals

In this paper, we propose a new flexible family of distributions for data that consist of three angles, two angles and one linear component, or one angle and two linear components. To achieve this, we equip the recently proposed trivariate wrapped Cauchy copula with non-uniform marginals and develop a parameter estimation procedure. We compare our model to its main competitors for analyzing trivariate data and provide some evidence of its advantages. We illustrate our new model using toroidal data from protein bioinformatics of conformational angles, and cylindrical data from climate science related to buoy in the Adriatic Sea. The paper is motivated by these real trivariate datasets.

stat.ME↗

arXiv2025

The trivariate wrapped Cauchy copula

In this paper, we propose a new flexible distribution for data on the three-dimensional torus which we call a trivariate wrapped Cauchy copula. Our trivariate copula has several attractive properties. It has a simple form of density and desirable modality properties. Its parameters allow for an adjustable degree of dependence between every pair of variables and these can be easily estimated. The conditional distributions of the model are well studied bivariate wrapped Cauchy distributions. Furthermore, the distribution can be easily simulated. Parameter estimation via maximum likelihood for the distribution is given and we highlight the simple implementation procedure to obtain these estimates. We illustrate our trivariate wrapped Cauchy copula on data from protein bioinformatics of conformational angles.

stat.ME↗

arXiv2025

Data-adaptive structural change-point detection via isolation

In this paper, a new data-adaptive method, called DAIS (Data Adaptive ISolation), is introduced for the estimation of the number and the location of change-points in a given data sequence. The proposed method can detect changes in various different signal structures; we focus on the examples of piecewise-constant and continuous, piecewise-linear signals. The novelty of the proposed algorithm comes from the data-adaptive nature of the methodology. At each step, and for the data under consideration, we search for the most prominent change-point in a targeted neighborhood of the data sequence that contains this change-point with high probability. Using a suitably chosen contrast function, the change-point will then get detected after being isolated in an interval. The isolation feature enhances estimation accuracy, while the data-adaptive nature of DAIS is advantageous regarding, mainly, computational complexity. The methodology can be applied to both univariate and multivariate signals. The simulation results presented indicate that DAIS is at least as accurate as state-of-the-art competitors and in many cases significantly less computationally expensive.

stat.ME↗