Noise-resilient penalty operators based on statistical differentiation schemes
基于统计微分方案的抗噪声惩罚算子
Classical approaches to penalized smoothing often rely on basis or kernel expansions, which constrain the estimator to a fixed span and may be restrictive for discretely observed data. We instead regularize a single noisy trajectory directly on its observation grid, using difference operators that remain genuine finite-difference approximations to derivatives while being statistically normalized and mutually decorrelated under a reference noise law. We extend this…