On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data

Springer Science and Business Media LLC - Tập 76 - Trang 49-81 - 2013
Jan Beran1, Arno Weiershäuser1, C. Giovanni Galizia2, Julia Rein2, Brian H. Smith3, Martin Strauch2
1Department of Mathematics and Statistics, University of Konstanz, Konstanz, Germany
2Department of Neurobiology, University of Konstanz, Konstanz, Germany
3School of Life Sciences, Arizona State University, Tempe, Arizona, USA

Tóm tắt

Motivated by the analysis of glomerular time series extracted from calcium-imaging data, asymptotic theory for piecewise polynomial and spline regression with partially free knots and residuals exhibiting three types of dependence structures (long memory, short memory and anti-persistence) is considered. Unified formulas based on fractional calculus are derived for subordinated residual processes in the domain of attraction of a Hermite process. The results are applied to testing for the effect of a neurotransmitter on the response of olfactory neurons in honeybees to odorant stimuli.

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