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December 2010 Nonparametric inference of doubly stochastic Poisson process data via the kernel method
Tingting Zhang, S. C. Kou
Ann. Appl. Stat. 4(4): 1913-1941 (December 2010). DOI: 10.1214/10-AOAS352


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.


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Tingting Zhang. S. C. Kou. "Nonparametric inference of doubly stochastic Poisson process data via the kernel method." Ann. Appl. Stat. 4 (4) 1913 - 1941, December 2010.


Published: December 2010
First available in Project Euclid: 4 January 2011

zbMATH: 1220.62037
MathSciNet: MR2829941
Digital Object Identifier: 10.1214/10-AOAS352

Keywords: arrival rate , asymptotic normality , autocorrelation function , Bandwidth selection , biophysical experiments , Cox process , short-range dependence

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.4 • No. 4 • December 2010
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