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

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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.

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
Do somebody tell me a best nano engineering book for beginners?
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
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
how did you get the value of 2000N.What calculations are needed to arrive at it
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Good
Berger describes sociologists as concerned with
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