On piecewise polynomial regression under general dependence conditions, with an application to calcium-imaging data. (English) Zbl 1305.62318
Summary: 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.
MSC:
| 62M09 | Non-Markovian processes: estimation |
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 60G22 | Fractional processes, including fractional Brownian motion |
| 62M99 | Inference from stochastic processes |
| 62J02 | General nonlinear regression |
Keywords:
long-range dependence; antipersistence; piecewise polynomial regression; spline regression; fractional calculus; fractional Brownian motion; Hermite process; calcium imaging; olfactionSoftware:
longmemoReferences:
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