Statistical and Actuarial Sciences Publications

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Nonparametric methods for smoothing, regression, and density estimation produce estimators with great shape flexibility. Although this flexibility is an advantage, the practical value of nonparametric methods would be increased if qualitative constraints—natural-language shape restrictions—could also be imposed on the estimator. In density estimation, the most common such constraints are monotonicity (the density must be nondecreasing or nonincreasing) and unimodality (the density must have only one peak). The work presented here takes unimodal kernel density estimation as a representative problem in constrained nonparametric estimation. The method proposed for handling the constraint is data sharpening. A greedy algorithm is described for achieving the unimodality constraint. The algorithm is deterministic and runs quickly. It can find solutions that are competitive with the incumbent method, sequential quadratic programming.


This is a technical report from the Department of Statistical and Actuarial Sciences. The posting of it was recommended by Dr. John Braun.