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Title: A characterization theorem for the least squares piecewise monotonic data fitting Authors:  Ioannis Demetriou - University of Athens (Greece) [presenting]
Abstract: Let a sequence of $n$ univariate observations that include random errors be given and let $k$ be a prescribed integer. The problem of calculating the least squares data fitting subject to the condition that the first differences of the estimated values have at most $k-1$ sign changes is considered. The choice of the positions of sign changes by considering all possible combinations of positions can be of magnitude $n^{k-1}$, so that it is not practicable to test each one separately. A theorem is stated that decomposes the problem into least squares monotonic estimation problems (case $k=1$) to disjoint sets of adjacent data. Besides that the theorem allows a highly efficient calculation of the piecewise monotonic estimates, it may be useful for investigating consistency properties of these estimates.