# 0.2 The impact of i.j. good on density estimation

 Page 1 / 2
One of three appreciations of I.J. Good's work published in The Good Book: Thirty Years of Conmments, Conjectures and Conclusions by I.J. Good. The book is available in print form from Rice University Press (http://ricepress.rice.edu).

(This module helps introduce The Good Book: Thirty Years of Comments, Conjectures and Conclusions, by I.J. Good . The book is available for purchase from the Rice University Press Store . You can also visit the Rice University Press web site .)

## Density estimation

It is a pleasure to review Jack Good's numerous contributions to the theory and practice of modern statistics.Here, we wish to remember his innovations in the field of nonparametric density estimation.Together with his student R. A. Gaskins, Jack invented penalized likelihood density estimation (Good and Gaskins, 1971).Given the computing resources available at that time, the implementation was truly revolutionary. A Fourier seriesapproximation was introduced, not with just a few terms, but ofttimes thousands of terms. To address the issue ofnonnegativity, the authors solved for the square root of the density. The penalty functions described were ${L}_{2}$ norms of the first and second derivatives of the density's square root.

The first author had the pleasure of attending a lecture by Jack at one of the early Southern Research Conference on Statisticsmeetings and returned to Rice University with a number of questions. For example, isthe square root “trick” valid? Could a closed-form solution be found? Considering such questions led to collaborationswith numerical analyst Richard Tapia and theses by Gilbert de Montricher and the second author. Gilbert wasable to show that the first derivative penalty could be solved in closed form. (Klonias [1982]later provided a wider set of solutions.) But Gilbert also showed that the squareroot trick does not work in general in infinite-dimensional Hilbert spaces, such as those considered here. Scott (1976)examined a finite-dimensional approximation for which the square-root trick does apply. These research findings werecollected in Tapia and Thompson (1978), one of the first surveys of nonparametric density estimation.In this and other venues, Jack's pioneering work led to a large body of research based on splines andother bases.

## Nonparametric density research at rice

Jack's inspiration came at a very fortuitous time for statisticians at Rice. NASA funding had switched from an emphasis on space exploration to that ofagricultural intelligence gathering via remote sensing. (Thompson well remembers Jack in his IDA days walking around Princetonin a trenchcoat, affecting the pose of George Smiley. So Jack might appreciate what follows below.)The idea was to identify and exploit shortages in Soviet grain production.

The NASA prototype solution in 1970 used a huge and clunky multi-spectral scanner that recorded groundreflectivity in twelve channels. This involved flyovers in Kansas from large aircraft.Misclassification rates were running around 25% using the assumption the data were multivariate Gaussian.The solution (before we got into the problem) was to expand the hardware to an even larger twenty-four-channel device.NASA had not run into the heavy-tailed pathologies dealt with by the Princeton Robustness Project, but rather into themixture of distributions problem which the Princetonians did not address. Of course, for the mixture problem under theGaussian assumption, things get worse as the number of channels increases. Thompson was somewhat amazed to find during adrive around in the summer of 1971 that the LARYS group at Purdue and the Willow Run group at Michigan were also treatingthe data as though they were Gaussian.

what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!