No Subject

[Pietro Muliere <pietro.muliere@uni-bocconi.it>]

Istituto Metodi Quantitativi - Università L. Bocconi
Viale Isonzo, 25 - 20135 Milano
Tel. 02-58365629  - Fax 02-58365630




SEMINARIO



SOME EXTREMAL PROBLEMS FOR GAUSSIAN
AND EMPIRICAL RANDOM FIELDS

                         Ya.Yu.Nikitin
Department of Mathematics and Mechanics
St. Petersburg University, Russia





giovedì, 3 maggio 2001 - ore 16.00
aula IMQ - stanza 137


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Abstract:
Some important problems of Probability and Statistics can be reduced  to 
the evaluation of supremum of some homogeneous functional defined on the 
Strassen ball in the space of smooth functions on the square. We give the 
solution of this extremal problem in two particular cases:  when the 
functional is linear and continuous and when it is a superposition of two 
seminorms. As a result we obtain the rough large deviation asymptotics 
for  Lp -norms of Brownian fields on the square, some Strassen type laws of 
iterated logarithm for functionals of Brownian fields, and describe the 
conditions of local Bahadur optimality for some nonparametric independence 
tests such as generalized rank correlation coefficients.