Smoothing unit vector fields |
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| Authors: | Carlos E Mendoza |
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| Institution: | (1) Dir. de Estadisticas de Corto Plazo, Insurgentes Sur 617, cuarto piso Col. Napoles, Mexico D.F., Mexico |
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| Abstract: | Data, each consisting of a unit vector and a position, are modeled as a smooth unit vector field plus random directional errors; the smooth unit vector field is estimated by fitting a spline to observations. The estimate is nonlinear; it is obtained with an iterative procedure in which, at each step, a least-squares smoothing spline is fitted to a set of pseudovalues. The resulting estimate is exemplified with a data set extracted from the literature in geology. The proposed estimate is compared, using the same data set with that obtained through suggestions of other authors, and is found to have attractive qualities. The use of plots of the resulting estimate to find the appropriate value of the smoothing parameter is emphasized throughout. |
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| Keywords: | directional data splines unit vector fields smoothing |
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