Drift Models on Complex Projective Space for Electron-Nuclear Double Resonance

TL;DR

This paper introduces a novel drift model for ENDOR spectroscopy, modeling spectra as elements of complex projective space, enabling improved analysis of thermal drifts and phase noise, with proven consistency and central limit theorems.

Contribution

It presents a pioneering parametric drift model on complex projective space for ENDOR spectra, extending Fréchet mean theory and providing rigorous statistical properties.

Findings

Model achieves better fit in practice.

Provides hypothesis testing and confidence intervals.

Improves signal-to-noise ratio over existing models.

Abstract

ENDOR spectroscopy is an important tool to determine the complicated three-dimensional structure of biomolecules and in particular enables measurements of intramolecular distances. Usually, spectra are determined by averaging the data matrix, which does not take into account the significant thermal drifts that occur in the measurement process. In contrast, we present an asymptotic analysis for the homoscedastic drift model, a pioneering parametric model that achieves striking model fits in practice and allows both hypothesis testing and confidence intervals for spectra. The ENDOR spectrum and an orthogonal component are modeled as an element of complex projective space, and formulated in the framework of generalized Fr\'echet means. To this end, two general formulations of strong consistency for set-valued Fr\'echet means are extended and subsequently applied to the homoscedastic drift model to prove strong consistency. Building on this, central limit theorems for the ENDOR spectrum are shown. Furthermore, we extend applicability by taking into account a phase noise contribution leading to the heteroscedastic drift model. Both drift models offer improved signal-to-noise ratio over pre-existing models.