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 journalArticlepeer-review

1 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 languageEnglish (US)
Pages (from-to)49-81
Number of pages33
JournalSankhya B
Volume76
Issue number1
DOIs
StatePublished - 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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