Nonparametric Estimation of Signals Corrupted by Noise with Sharp Peaks

Filters analogous to $L$- and $M$-estimators of an unknown location parameter of a distribution are proposed for estimating a deterministic continuous-time signal from noisy observations. Assuming white noise, we prove that the proposed estimators are asymptotically normal for a finite observation period. The estimators have finite bias and variance even when the noise is of infinite variance. Minimax optimization of the procedures is considered.