论文标题
始终从嘈杂的功能数据中恢复信号
Consistently recovering the signal from noisy functional data
论文作者
论文摘要
实际上，大多数功能数据不能记录在连续性上，而是在离散的时间点上记录。这些测量值也带有一个添加剂误差，这也很常见，这对于统计分析而言需要消除。当在同一网格上进行每个功能基准的测量值时，可以将基础信号加上噪声模型视为因素模型。信号是指因子模型的共同组成部分，噪声与特质组件有关。我们制定了一个框架，该框架允许通过基于PCA的因子模型估计方案始终如一地恢复信号。我们的理论结果在相当温和的条件下成立，特别是我们不需要针对基础曲线的特定平滑度假设，并且可以在噪声中具有一定程度的自相关性。
In practice most functional data cannot be recorded on a continuum, but rather at discrete time points. It is also quite common that these measurements come with an additive error, which one would like eliminate for the statistical analysis. When the measurements for each functional datum are taken on the same grid, the underlying signal-plus-noise model can be viewed as a factor model. The signals refer to the common components of the factor model, the noise is related to the idiosyncratic components. We formulate a framework which allows to consistently recover the signal by a PCA based factor model estimation scheme. Our theoretical results hold under rather mild conditions, in particular we don't require specific smoothness assumptions for the underlying curves and allow for a certain degree of autocorrelation in the noise.
