0.2 The impact of i.j. good on density estimation  (Page 2/2)

At Rice we immediately discovered that we could gain dramatic improvements (misclassification rates of 5%) by dropping the number ofchannels to four and using template methods. We quickly moved to kernel approaches. Some years later, the NASA group, led byRichard Heydorn, took the solution for a four-channel scanner and easily packaged it into a satellite. They had arrived at apoint where NASA forecasting of Soviet grain production was much better than that of the Soviet Ministry of Agriculture. Thetechnology was exploited, according to the terms of the Jackson-Vanik Amendment, to trade the permission of the Soviets intheir unusually bad years (there were no good years) to buy US grain at spot prices in exchange for very relaxed policies on theemigration of Soviet Jews to Israel. Thus, nonparametric density estimation has had indirect but dramatic effects on thedemographics of Israel. Jackson-Vanik has permitted hundreds of thousands of Soviet Jews to resettle in Israel. Without theNASA results, Jackson-Vanik would have had no teeth.

We expanded our research to work on Defense modeling, ecology, and biomedical work in cardiology and oncology.Over the years, Rice has produced over a hundred papers, three books, and dozens of doctorates in nonparametric functionestimation topics in a variety of application areas.

Bump hunting

One of the most important applications of density estimation is the discovery and characterization of features. In Goodand Gaskins (1980), the authors set forth an extremely influential application of their penalized likelihood estimator for assigning odds for the veracity of modes and bumps.Silverman (1981) introduced a bootstrap technique that examines the number of modes in a density all at once.However, Good and Gaskins examined individual modes (and more generally, bumps) one-at-a-time, which webelieve is the more powerful approach. One would like to find the “closest” density without the mode or bumpof interest. What the authors introduced was “bump surgery,” where the raw data were gently massaged toreduce the size of the mode or bump, until it was just eliminated. Then a quantity rather like log-likelihoodcould be computed to quantify the odds on whether the feature is real, or just an artifact of the sample. This problem isvery challenging, and many lines of research have ensued. But the paper was read at the Joint StatisticalMeetings, accompanied by a lively set of discussions, and has been enormously influential in the field.

Appreciation

The second author had the pleasure of serving as Jack Good's chauffeur twice. At another SRCOS meeting in Arkansas, Jackflew into a nearby airport. The SRCOS meetings were a wonderful week-long affair that made research discussionsinformal and exciting. In 1993, Jack was invited to give a talk at the National Security Agency, where thethe second author was spending a sabbatical. Jack agreed to visit if he did not have to drive. A large collection of Jack's classifiedpublications are available in the NSA library, typewritten with 1940s technology. Many of Jack's friends hadlong retired from NSA, but the excitement of problem- solving made for a memorable day.

Thus it is our great pleasure to share in the celebration of Jack's ninetieth birthday and to admire the depth and breadth ofhis work. Many happy returns.

References

Good, I. J. and Gaskins, R. A. (1971), “Nonparametric roughness penalties for probability densities,”Biometrika , 58, 255-277.

Good, I. J. and Gaskins, R. A. (1980), “Density estimation and bump-hunting by the penalized likelihoodmethod exemplified by scattering and meteorite data,” J. Amer Stat Assoc, 75, 42-56.

Klonias, V. K. (1982), “Consistency of two nonparametric maximum penalized likelihood estimators of the probability density function,”Annals of Statistics , 10, 811-824.

Scott, D.W. (1976), “Nonparametric Probability Density Estimation by Optimization Theoretic Techniques,” unpublished doctoral dissertation,Rice University, Houston.

Silverman, B. W. (1981), “Using kernel density estimates to investigate multimodality,” J. Royal Statistical Society, Series B,43, 97-99.

Tapia, R. A. and Thompson, J.R. (1978), Nonparametric probability density estimation, Johns Hopkins University Press, Baltimore.