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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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Beran, J., Weiershäuser, A., Galizia, C.G. et al. On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data. Sankhya B 76, 49–81 (2014). https://doi.org/10.1007/s13571-013-0066-3

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  • DOI: https://doi.org/10.1007/s13571-013-0066-3

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