论文标题
自适应minimax测试进行圆形卷积
Adaptive minimax testing for circular convolution
论文作者
论文摘要
鉴于从添加剂测量误差污染的圆形随机变量的观察结果，我们考虑了最小值最佳拟合优度测试的问题。我们使用投影方法提出了直接和间接测试程序。最佳测试的结构取决于模型的规律性和不适合性参数，在实践中是未知的。因此，同时研究了在广泛的规律性和适应性不良类别中最佳性能的自适应测试策略。考虑到多个测试程序，我们获得自适应，即无假设程序并分析其性能。与非自适应测试相比，它们的测试半径面临对数因子的恶化。我们表明，对于均匀性测试，通过提供下限是不可避免的。考虑到Sobolev空间以及普通或超级平滑误差密度，结果说明了结果。
Given observations from a circular random variable contaminated by an additive measurement error, we consider the problem of minimax optimal goodness-of-fit testing in a non-asymptotic framework. We propose direct and indirect testing procedures using a projection approach. The structure of the optimal tests depends on regularity and ill-posedness parameters of the model, which are unknown in practice. Therefore, adaptive testing strategies that perform optimally over a wide range of regularity and ill-posedness classes simultaneously are investigated. Considering a multiple testing procedure, we obtain adaptive i.e. assumption-free procedures and analyse their performance. Compared with the non-adaptive tests, their radii of testing face a deterioration by a log-factor. We show that for testing of uniformity this loss is unavoidable by providing a lower bound. The results are illustrated considering Sobolev spaces and ordinary or super smooth error densities.
