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

Jan Beran; Arno Weiershäuser; C. Giovanni Galizia; Julia Rein; Brian Smith; Martin Strauch

doi:10.1007/s13571-013-0066-3

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

Jan Beran, Arno Weiershäuser, C. Giovanni Galizia, Julia Rein, Brian Smith, Martin Strauch

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	49-81
Number of pages	33
Journal	Sankhya B
Volume	76
Issue number	1
DOIs	https://doi.org/10.1007/s13571-013-0066-3
State	Published - May 1 2014

Keywords

Hermite process
Long-range dependence
antipersistence
calcium imaging
fractional Brownian motion
fractional calculus
olfaction
piecewise polynomial regression
spline regression

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1007/s13571-013-0066-3

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

abstract = "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.",

keywords = "Hermite process, Long-range dependence, antipersistence, calcium imaging, fractional Brownian motion, fractional calculus, olfaction, piecewise polynomial regression, spline regression",

author = "Jan Beran and Arno Weiersh{\"a}user and Galizia, {C. Giovanni} and Julia Rein and Brian Smith and Martin Strauch",

note = "Funding Information: Acknowledgement. This work was supported in part by BMBF grant FKZ01GQ0771 to CGG, MS, JR. MS is an associated member of the DFG Research Training Group GK-1042 “Explorative Analysis and Visualization of Large Information Spaces”. Moreover, this research was also partially funded by NIH NCRR grants RR014166, RR014166S1 and NIDCD grant DC007997 to BHS. We would like to thank the referees for their insightful comments. Publisher Copyright: {\textcopyright} 2013, Indian Statistical Institute.",

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doi = "10.1007/s13571-013-0066-3",

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AU - Beran, Jan

AU - Weiershäuser, Arno

AU - Galizia, C. Giovanni

AU - Rein, Julia

AU - Smith, Brian

AU - Strauch, Martin

N1 - Funding Information: Acknowledgement. This work was supported in part by BMBF grant FKZ01GQ0771 to CGG, MS, JR. MS is an associated member of the DFG Research Training Group GK-1042 “Explorative Analysis and Visualization of Large Information Spaces”. Moreover, this research was also partially funded by NIH NCRR grants RR014166, RR014166S1 and NIDCD grant DC007997 to BHS. We would like to thank the referees for their insightful comments. Publisher Copyright: © 2013, Indian Statistical Institute.

PY - 2014/5/1

Y1 - 2014/5/1

N2 - 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.

AB - 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.

KW - Hermite process

KW - Long-range dependence

KW - antipersistence

KW - calcium imaging

KW - fractional Brownian motion

KW - fractional calculus

KW - olfaction

KW - piecewise polynomial regression

KW - spline regression

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

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Keywords

ASJC Scopus subject areas

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