| Decreasing and unimodal density estimation using shape-restricted regression splines
| Mary C. Meyer
Ph.D., University of Georgia
Monday, February 5, 2007
Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the estimators are more robust to knot choices. Shape-restricted regression splines can also be applied to the desnity estimation problem. They provide smoothed estimates for densities that are assumed to be either decreasing or unimodal, and are also robust compared with the unrestricted versions. Algorithms using cone projection are presented and consistency results are discussed.