NSF Award
9628595
*** 9628595 Andrew G. Bruce This Small Business Innovation Research Phase II project has the ultimate objective of developing an object-oriented software toolkit for wavelet based nonparametric prediction. The current theory and practice of nonparametric estimation with wavelets is limited to a small set of prediction problems. Statistical prediction or function estimation is of fundamental importance, with applications to a broad range of problems. In the overwhelming majority of situations, non-parametric prediction methods are the most appropriate. Based on the wavelet transform, Donoho and Johnstone have developed a powerful methodology, called "WaveShrink", for nonparametric function estimation. WaveShrink has a very broad asymptotic near-optimality property and has proven valuable in practice. The project will address itself to fundamental advancements that are needed to develop new wavelet methodology encompassing a much broader set of prediction problems. The new and existing methodology will be collected into a coherent object-oriented software toolkit. This toolkit will be of use to a broad range of statisticians, data analysts, scientists, and engineers. The research will lead to a completely new version of the S-Plus software module S+Wavelets. Other commercial opportunities include consulting and teaching, a Mathcad function pack and electronic book, software licensing and patenting innovative algorithms. ***
