Doubly stochastic Poisson processes, also known as the Cox processes,
frequently occur in various scientific fields. In this article, motivated
primarily by analyzing Cox process data in biophysics, we propose a
nonparametric kernel-based inference method. We conduct a detailed study,
including an asymptotic analysis, of the proposed method, and provide
guidelines for its practical use, introducing a fast and stable regression
method for bandwidth selection. We apply our method to real photon arrival data
from recent single-molecule biophysical experiments, investigating proteins'
conformational dynamics. Our result shows that conformational fluctuation is
widely present in protein systems, and that the fluctuation covers a broad
range of time scales, highlighting the dynamic and complex nature of proteins'
structure.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS352 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org