In many ways, Sid Yakowitz has provided the inspiration, pioneering contributions and theoretical background for the type of research reported here. His contributions, motivated by hydrologic problems, predate the recent interest in this subject in the statistical community.
Historically, the nonparametric function estimation literature has been largely very mathematical. Yet, the idea of a moving average (isn't that what this is all about?) is quite palatable and routinely indulged in by practitioners. Here, finally, are techniques that formally allow one to use it with some theoretical basis. But...but, you can't extrapolate using a moving average, now can you? Well, that's why success in flood frequency analysis was given much press. For this reporter, a wonderful thing about turning to this literature has been learning how estimation techniques (parametric and non) come together in a unified manner, from a geometrical point of view, from the perspective of approximation and measure theory, and enable data visualization. It is exciting to sidestep model choice issues, work directly with functions of interest to the decision maker, visually see the relationships in the data set clarified, without paying a high price for this flexibility, and be part of an evolving area.
Acknowledgments. The author is grateful to the U.S.G.S., the Utah Division of Water Rights, and the U.S. Forest Service, for support of his nonparametric research. Thanks are due to a number of colleagues for making this a rewarding learning experience; and to S. Yakowitz and K. Adamowski for originating the author's interest in the subject. The comments of the anonymous reviewers helped improve this manuscript.