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SUMMARY:On sufficient conditions for implementing the functional approach 
 - Melas\, VB (Saint-Petersburg State University)
DTSTART:20110719T080000Z
DTEND:20110719T090000Z
UID:TALK32090@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:Let us consider the general nonlinear regression model under s
 tandard assumptions on the experimental errors. Let also the following ass
 umptions be fulfilled: (i) the regression function depends on a scalar var
 iable belonging to the design interval\, (ii) the derivatives of the funct
 ion with respect to the parameters generate an extended Chebyshev system o
 n the design interval\, (iii) the matrix of second derivatives of the opti
 mality criterion with respect to the different information matrix elements
  is positive definite. Then under non-restrictive assumptions it can be pr
 oved that the Jacobi matrix of the system of differential equations that d
 efines implicitly support points and weight coefficients of the optimal de
 sign is invertible. This allows us to implement the Implicit Function Theo
 rem for representing the points and the weights by a Taylor series. The co
 rresponding theorems as well as particular examples of nonlinear models ar
 e elaborated. The results are generalisations of those given in the monogr
 aph published recently by the author. \n
LOCATION:Seminar Room 1\, Newton Institute
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