论文标题
在非平稳函数值分析过程中量化与结构假设偏差的一般框架
A general framework to quantify deviations from structural assumptions in the analysis of nonstationary function-valued processes
论文作者
论文摘要
我们提出了一种一般理论，可以量化对非组织希尔伯特太空值过程的二阶结构施加结构假设的不确定性，该过程可以通过时间依赖性频谱密度运算符的功能来衡量。二阶动力学是众所周知的，是痕迹运算符空间的要素，后者是类型1和Cotype 2的Banach空间，这使得统计推理工具的开发更具挑战性。我们的贡献的一部分是获得弱的不变性原理以及（功能）的（功能）顺序变化的光谱密度运算符。此外，我们在非组织环境中引入偏差度量，并导出渐近关键的估计器。然后，我们应用该框架并提出统计方法来研究非平稳响应表面数据的结构假设的有效性，例如在时间变化的动态FPCA的背景下低排名的假设和原理可分离组件分析，与平方根距离相对于平方根距离的偏差，以及偏离零功能均方根均方根的偏差。
We present a general theory to quantify the uncertainty from imposing structural assumptions on the second-order structure of nonstationary Hilbert space-valued processes, which can be measured via functionals of time-dependent spectral density operators. The second-order dynamics are well-known to be elements of the space of trace-class operators, the latter is a Banach space of type 1 and of cotype 2, which makes the development of statistical inference tools more challenging. A part of our contribution is to obtain a weak invariance principle as well as concentration inequalities for (functionals of) the sequential time-varying spectral density operator. In addition, we introduce deviation measures in the nonstationary context, and derive estimators that are asymptotically pivotal. We then apply this framework and propose statistical methodology to investigate the validity of structural assumptions for nonstationary response surface data, such as low-rank assumptions in the context of time-varying dynamic fPCA and principle separable component analysis, deviations from stationarity with respect to the square root distance, and deviations from zero functional canonical coherency.
