Given a scatterplot of \((x_i, y_i)\), \(i = 1,\ldots,n\), where \(\bold{x}\) could be a vector of years and \(\bold{y}\) could be a vector of Landsat signals, constrained least-squares spline fits are obtained for the following shapes:
1. flat
2. decreasing
3. one-jump, i.e., decreasing, jump up, decreasing
4. inverted vee (increasing then decreasing)
5. vee (decreasing then increasing)
6. linear increasing
7. double-jump, i.e., decreasing, jump up, decreasing, jump up, decreasing.
The shape with the smallest information criterion may be considered a "best" fit. This shape-selection problem was motivated by a need to identify types of disturbances to areas of forest, given Landsat signals over a number of years. The satellite signal is constant or slowly decreasing for a healthy forest, with a jump upward in the signal caused by mass destruction of trees.
The main routine to select the shape for a scatterplot is "shape". See shape for more details.
Mary C. Meyer, Xiyue Liao, Elizabeth Freeman, Gretchen G. Moisen
Maintainer: Xiyue Liao <xiyue@rams.colostate.edu>
Meyer, M. C. and Woodroofe M (2000) On the Degrees of Freedom in Shape-Restricted Regression. The Annals of Statistics 28, 1083--1104.
Meyer, M. C. (2013a) Semi-parametric additive constrained regression. Journal of Nonparametric Statistics 25(3), 715.
Meyer, M. C. (2013b) A simple new algorithm for quadratic programming with applications in statistics. Communications in Statistics 42(5), 1126--1139.
Liao, X. and M. C. Meyer (2014) coneproj: An R package for the primal or dual cone projections with routines for constrained regression. Journal of Statistical Software 61(12), 1--22.