Title: Robust and Efficient Parametric Spectral Estimation in Atomic Force Microscopy,
Abstract: An atomic force microscope (AFM) is capable of producing ultra-high
resolution measurements of nanoscopic objects and forces. It is an
indispensable tool for various scientific disciplines such as molecular
engineering, solid-state physics, and cell biology. Prior to a given
experiment, the AFM must be calibrated by fitting a spectral density model to
baseline recordings. However, since AFM experiments typically collect large
amounts of data, parameter estimation by maximum likelihood can be
prohibitively expensive. Thus, practitioners routinely employ a much faster
least-squares estimation method, at the cost of substantially reduced
statistical efficiency. Additionally, AFM data is often contaminated by
periodic electronic noise, to which parameter estimates are highly sensitive.
This article proposes a two-stage estimator to address these issues.
Preliminary parameter estimates are first obtained by a variance-stabilizing
procedure, by which the simplicity of least-squares combines with the
efficiency of maximum likelihood. A test for spectral periodicities then
eliminates high-impact outliers, considerably and robustly protecting the
second-stage estimator from the effects of electronic noise. Simulation and
experimental results indicate that a two- to ten-fold reduction in mean squared
error can be expected by applying our methodology.