紧致黎曼流形上一致性的数据驱动Sobolev检验

紧黎曼流形上分布拟合优度的Sobolev检验

Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds

提出了紧致黎曼流形上坐标不变的综合拟合优度检验类。该测试基于Giné的Sobolev均匀性测试。给出了一致性的一个条件。通过旋转群$\mathit{SO}(3)$上的一个示例说明了测试。

超球面上的高维Sobolev检验

High-dimensional Sobolev tests on hyperspheres

研究超球面上均匀性的Sobolev检验，推导其在维度和样本量趋于无穷时的极限零分布，探讨极限非零行为，包括一致性结果和渐近功效，应用于高维对称性检验及实际数据，数值实验验证了检验行为。

克服数据驱动的Sobolev检验在超球面上的对称性盲区

Addressing parity blindness of data-driven Sobolev tests on the hypersphere

本文提出改进的数据驱动Sobolev检验，以克服超球面上检验均匀性时对连续替代假设的盲区问题。

关于超球面上均匀性的Stein检验

On Stein's test of uniformity on the hypersphere

提出基于Laplace-Beltrami算子的Stein特征检验超球面均匀性，利用Gegenbauer多项式调和分解，导出检验统计量的渐近分布，并通过调节参数增强对多种备择假设的检验功效。

On a projection-based class of uniformity tests on the hypersphere

We propose a projection-based class of uniformity tests on the hypersphere using statistics that integrate, along all possible directions, the weighted quadratic discrepancy between the empirical cumulative distribution function of the projected data and the projected uniform distribution. Simple expressions for several test statistics are obtained for the circle and sphere, and relatively tractable forms for higher dimensions. Despite its different origin, the proposed class is shown to be related with the well-studied Sobolev class of uniformity tests. Our new class proves itself advantageou…