Isotonic, Convex and Related Splines.
NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS
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The estimation of isotonic, convex or related functions is considered by means of splines. It is shown that certain classes of isotone or convex functions can be represented as a positive cone embedded in a Hilbert space. Using this representation, an existence and characterization theorem are given for isotonic or convex splines. Two special cases are examined showing the existence of a globally monotone cubic smoothing spline and a globally convex quintic smoothing spline. Finally, a regression problem is examined and shows that the isotonic-type of spline provides a strongly consistent solution. Several other statistical applications are given.
- Statistics and Probability