Stochastic Spline Functions with Unequal Time Steps

Authors: Stephen P. Smith

A piece-wise quadratic spline is introduced as a time series coming with unequal time steps, and where the second derivative of the spline at the junction points is impacted by random Brownian motion. A measurement error is also introduced, and this changes the spline into semi-parametric regression. This makes a total of two dispersion parameters to be estimated by a proposed REML analysis that unitizes the K-matrix. The spline itself only has three location effects that are treated as fixed, and must be estimated. A proposed prediction of a future observation beyond the spline’s end point is presented, coming with a prediction error variance.

Comments: 13 Pages.

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Submission history

[v1] 2018-09-02 17:36:12

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