Change-Point estimation using shape-restricted regression splines
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Change-Point estimation is in need in fields like climate change, signal processing, economics, dose-response analysis etc, but it has not yet been fully discussed. We consider estimating a regression function ƒm and a change-point m, where m is a mode, an inflection point, or a jump point. Linear inequality constraints are used with spline regression functions to estimate m and ƒm simultaneously using profile methods. For a given m, the maximum-likelihood estimate of ƒm is found using constrained regression methods, then the set of possible change-points is searched to find the ˆm that maximizes ...