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Sankhya B

, Volume 76, Issue 1, pp 49–81 | Cite as

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 H. Smith
  • Martin Strauch
Article
  • 151 Downloads

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

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

AMS (2000) subject classification.

Primary 62M09 62M10 60G22 Secondary 62M99 62J02 

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Copyright information

© Indian Statistical Institute 2013

Authors and Affiliations

  • Jan Beran
    • 1
  • Arno Weiershäuser
    • 1
  • C. Giovanni Galizia
    • 2
  • Julia Rein
    • 2
  • Brian H. Smith
    • 3
  • Martin Strauch
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of KonstanzKonstanzGermany
  2. 2.Department of NeurobiologyUniversity of KonstanzKonstanzGermany
  3. 3.School of Life SciencesArizona State University TempeArizonaUSA

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