On spline regression under Gaussian subordination with long memory. (English) Zbl 1327.62459
Summary: Motivated by an example from neurobiology, we consider estimation in a spline regression model with long-range dependent errors that are generated by Gaussian subordination. Consistency and the asymptotic distribution are derived for general Hermite ranks. Simulations illustrate the asymptotic results and finite sample properties. The method is applied to optical measurements of calcium concentration in the antennal lobe of honey bees used in the study of olfactory patterns.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F12 | Asymptotic properties of parametric estimators |
| 62J02 | General nonlinear regression |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 62M09 | Non-Markovian processes: estimation |
Keywords:
long-range dependence; Hermite rank; Gaussian subordination; spline regression; two-phase regression; change pointSoftware:
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