Semiparametric curve alignment and shift density estimation for biological data

TL;DR

This paper introduces a novel semiparametric method for aligning biological curves and estimating the distribution of their unknown time shifts, demonstrating robustness and improved performance over existing methods.

Contribution

The authors propose a three-stage M-estimator algorithm for shift estimation and density estimation, applicable to biological data with unknown pulse shapes.

Findings

Estimator performs well at low signal-to-noise ratios

Method outperforms standard curve alignment techniques

Converges weakly to the true shift distribution

Abstract

Assume that we observe a large number of curves, all of them with identical, although unknown, shape, but with a different random shift. The objective is to estimate the individual time shifts and their distribution. Such an objective appears in several biological applications like neuroscience or ECG signal processing, in which the estimation of the distribution of the elapsed time between repetitive pulses with a possibly low signal-noise ratio, and without a knowledge of the pulse shape is of interest. We suggest an M-estimator leading to a three-stage algorithm: we split our data set in blocks, on which the estimation of the shifts is done by minimizing a cost criterion based on a functional of the periodogram; the estimated shifts are then plugged into a standard density estimator. We show that under mild regularity assumptions the density estimate converges weakly to the true shift distribution. The theory is applied both to simulations and to alignment of real ECG signals. The estimator of the shift distribution performs well, even in the case of low signal-to-noise ratio, and is shown to outperform the standard methods for curve alignment.