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 journalArticle

Abstract

Motivated by the analysis of glomerular time series extracted from calciumimaging 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: The Indian Journal of Statistics
Volume76B
StatePublished - 2014

Keywords

  • Antipersistence
  • Calcium imaging
  • Fractional Brownian motion
  • Fractional calculus
  • Hermite process
  • Long-range dependence
  • Olfaction
  • Piecewise polynomial regression
  • Spline regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Fingerprint Dive into the research topics of 'On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data'. Together they form a unique fingerprint.

  • Cite this