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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On sufficient conditions for implementing the func
tional approach - Melas\, VB (Saint-Petersburg Sta
te University)
DTSTART;TZID=Europe/London:20110719T090000
DTEND;TZID=Europe/London:20110719T100000
UID:TALK32090AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/32090
DESCRIPTION:Let us consider the general nonlinear regression m
odel under standard assumptions on the experimenta
l errors. Let also the following assumptions be fu
lfilled: (i) the regression function depends on a
scalar variable belonging to the design interval\,
(ii) the derivatives of the function with respect
to the parameters generate an extended Chebyshev
system on the design interval\, (iii) the matrix o
f second derivatives of the optimality criterion w
ith respect to the different information matrix el
ements is positive definite. Then under non-restri
ctive assumptions it can be proved that the Jacobi
matrix of the system of differential equations th
at defines implicitly support points and weight co
efficients of the optimal design is invertible. Th
is allows us to implement the Implicit Function Th
eorem for representing the points and the weights
by a Taylor series. The corresponding theorems as
well as particular examples of nonlinear models ar
e elaborated. The results are generalisations of t
hose given in the monograph published recently by
the author. \n
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:Mustapha Amrani
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