Mathematical Sciences: Mathematical Statistics on Singular Problems

奇异函数估计问题涵盖了一个极其复杂的 大部分统计理论。 一些程序， 最佳利率已经确立;但最近的工作， 白色噪声问题导致了基于 函数的模。 这种方法提供了最佳或接近 最佳程序相当简单的许多重要的统计 问题 对于某些统计估计问题， 众所周知，但对于更多的人来说， 方法不确定或其效率未知。 这 研究将产生普遍有效的程序， 有许多科学应用，例如复杂的问题 例如从断层摄影或其它方法重建“真实图像” 成像技术。这种统一的估算方法应 在工程学、生物学、经济学和其他领域找到应用 实践和理论科学问题的领域 用统计模型来描述。

Singular functional estimation problems cover an extremely large portion of statistical theory. Some procedures with optimal rates have been well established; but recent work on white noise problems has led to a unified approach based on the modulus of the functional. This approach gives optimal or near optimal procedures quite simply for many important statistical problems. For some statistical estimation problems, optimal methods are well known, but for many more either optimality of the methodology is uncertain or its efficiency is unknown. This research will produce generally efficient procedures which can have many scientific applications, for example complex problems like reconstruction of the "true image" from tomography or other imaging techniques. This unified approach to estimation should find applications in engineering, biology, economics and other fields where practical and theoretical scientific problems are framed in terms of statistical models.