arXiv subjects

Alberto Fernández-de-Marcos

Publications and source records attributed to Alberto Fernández-de-Marcos.

4 recordsLinked to original sources

arXiv2026

On new omnibus tests of uniformity on the hypersphere

Two new omnibus tests of uniformity for data on the hypersphere are proposed. The new test statistics exploit closed-form expressions for orthogonal polynomials, feature tuning parameters, and are related to a "smooth maximum" function and the Poisson kernel. We obtain exact moments of the test statistics under uniformity and rotationally symmetric alternatives, and give their null asymptotic distributions. We consider approximate oracle tuning parameters that maximize the power of the tests against known generic alternatives and provide tests that estimate oracle parameters through cross-validated procedures while maintaining the significance level. Numerical experiments explore the effectiveness of null asymptotic distributions and the accuracy of inexpensive approximations of exact null distributions. A simulation study compares the powers of the new tests with other tests of the Sobolev class, showing the benefits of the former. The proposed tests are applied to the study of the (seemingly uniform) nursing times of wild polar bears.

stat.ME↗

arXiv2026

A class of nonparametric homogeneity tests on the circle

We develop a unified framework for $c$-sample homogeneity testing on the circle. The proposed class of $c$-sample Sobolev tests generalizes the two-sample Sobolev tests based on uniform scores and encompasses the existing multisample tests as particular cases. We further embed this class into a broader aggregation framework, where the samplewise Sobolev components are combined through general merging functions, including average-type, maximum-type, and interpolating families. Within this class, we introduce the first Anderson-Darling-type homogeneity test for circular data, and we further propose two new tests designed to detect multimodal departures from homogeneity, constructed from softmax and Poisson kernels. We derive the asymptotic null distribution of the class, prove its consistency against a broad family of fixed alternatives, and obtain the asymptotic distribution under shift-type local alternatives. The tests are distribution-free and therefore do not require resampling. A comprehensive simulation study demonstrates the strong power of the Anderson-Darling-type test compared with Cramér-von Mises-type competitors across several scenarios, and the effectiveness of the softmax and Poisson tests under several alternatives. The testing toolbox is applied to analyze the nursing patterns of polar bears.

math.ST↗

arXiv2024

A stereographic test of spherical uniformity

We introduce a test of uniformity for (hyper)spherical data motivated by the stereographic projection. The closed-form expression of the test statistic and its null asymptotic distribution are derived using Gegenbauer polynomials. The power against rotationally symmetric local alternatives is provided, and simulations illustrate the non-null asymptotic results. The stereographic test outperforms other tests in a testing scenario with antipodal dependence between observations.

math.ST↗

arXiv2023

Data-driven stabilizations of goodness-of-fit tests

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 form of a lookup table or carried out on demand, to apply a goodness-of-fit test. There exist simple and useful transformations of several classic goodness-of-fit test statistics that stabilize their exact-$n$ critical values for varying sample sizes $n$. However, detail on the accuracy of these and subsequent transformations in yielding exact $p$-values, or even deep understanding on the derivation of several transformations, is still scarce nowadays. The latter stabilization approach is explained and automated to (i) expand its scope of applicability and (ii) yield upper-tail exact $p$-values, as opposed to exact critical values for fixed significance levels. Improvements on the stabilization accuracy of the exact null distributions of the Kolmogorov-Smirnov, Cramér-von Mises, Anderson-Darling, Kuiper, and Watson test statistics are shown. In addition, a parameter-dependent exact-$n$ stabilization for several novel statistics for testing uniformity on the hypersphere of arbitrary dimension is provided. A data application in astronomy illustrates the benefits of the advocated stabilization for quickly analyzing small-to-moderate sequentially-measured samples.

stat.ME↗