Mathematical programming algorithms for regression-based nonlinear filtering in RN

| This paper is concerned with regression under a \sum" of partial order constraints. Examples include locally monotonic, piecewise monotonic, runlength constrained, and uni-and oligo-modal regression. These are of interest in nonlinear ltering, but also in density estimation and chromatographic analysis. It is shown that, under a least absolute error criterion, these problems can be transformed into appropriate nite problems, which can then be eeciently solved via dynamic programming techniques. Although the result does not carry over to least squares regression , hybrid programming algorithms can be developed to solve least squares counterparts of certain problems in the class.