On Stein's test of uniformity on the hypersphere
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917291690557440 |
|---|---|
| author | Axmann, Paul Ebner, Bruno García-Portugués, Eduardo |
| author_facet | Axmann, Paul Ebner, Bruno García-Portugués, Eduardo |
| contents | We propose a new test of uniformity on the hypersphere based on a Stein characterization associated with the Laplace--Beltrami operator. We identify a sufficient class of test functions for this characterization, linked to the moment generating function. Exploiting the operator's eigenfunctions to obtain a harmonic decomposition in terms of Gegenbauer polynomials, we show that the proposed procedure belongs to the class of Sobolev tests. We derive closed-form expressions for the distribution of the test statistic under the null hypothesis and under fixed alternatives. To enhance power against a range of alternatives, we introduce a tuning parameter into the characterization and study its impact on rejection probabilities. We discuss data-driven strategies for selecting this parameter to maximize rejection rates for a given alternative and compare the resulting performance with that of related parametric tests. Additional numerical experiments compare the proposed test with competing Sobolev-class procedures, highlighting settings in which it offers clear advantages. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_20896 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Stein's test of uniformity on the hypersphere Axmann, Paul Ebner, Bruno García-Portugués, Eduardo Statistics Theory Methodology 62G10, 62H11 We propose a new test of uniformity on the hypersphere based on a Stein characterization associated with the Laplace--Beltrami operator. We identify a sufficient class of test functions for this characterization, linked to the moment generating function. Exploiting the operator's eigenfunctions to obtain a harmonic decomposition in terms of Gegenbauer polynomials, we show that the proposed procedure belongs to the class of Sobolev tests. We derive closed-form expressions for the distribution of the test statistic under the null hypothesis and under fixed alternatives. To enhance power against a range of alternatives, we introduce a tuning parameter into the characterization and study its impact on rejection probabilities. We discuss data-driven strategies for selecting this parameter to maximize rejection rates for a given alternative and compare the resulting performance with that of related parametric tests. Additional numerical experiments compare the proposed test with competing Sobolev-class procedures, highlighting settings in which it offers clear advantages. |
| title | On Stein's test of uniformity on the hypersphere |
| topic | Statistics Theory Methodology 62G10, 62H11 |
| url | https://arxiv.org/abs/2602.20896 |