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.",

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AU - Beran, Jan

AU - Weiershäuser, Arno

AU - Galizia, C. Giovanni

AU - Rein, Julia

AU - Smith, Brian

AU - Strauch, Martin

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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.

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KW - Long-range dependence

KW - antipersistence

KW - calcium imaging

KW - fractional Brownian motion

KW - fractional calculus

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

Abstract

Keywords

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