BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//wp-events-plugin.com//7.2.3.1//EN
TZID:Europe/Paris
X-WR-TIMEZONE:Europe/Paris
BEGIN:VEVENT
UID:6258@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20211122T140000
DTEND;TZID=Europe/Paris:20211122T140000
DTSTAMP:20241120T201348Z
URL:https://www.i2m.univ-amu.fr/evenements/minimax-estimation-of-nonlinear
 -functionals-of-a-density-via-construction-of-probability-measures-with-pr
 escribed-properties/
SUMMARY:Oleg Lepski (Pr. I2M AMU): Minimax estimation of nonlinear function
 als of a  density via  construction of probability measures with prescribe
 d properties
DESCRIPTION:Oleg Lepski: In this talk I discuss the minimax estimation of i
 ntegral-type functionals of a probability density. In the first part  I p
 resent the construction of  the lower bound of minimax risk on an arbitra
 ry set of functions. This construction is mostly based on the following pr
 inciples.\nFirst\, the original original estimation is reduced  to a prob
 lem of testing two composite hypotheses for mixture distributions which ar
 e obtained by imposing prior probability measures with intersecting suppor
 ts on parameters of a\nfunctional family. These couple of measures should 
 possess several properties and their construction\,\nbasing on the notion 
 of the best approximation of continuous functions\, has an independent int
 erest. In particular\, the moment matching technique can be mentioned in t
 his context.\nThe second idea is related to construction of a specific par
 ameterized family of densities on\nwhich the lower bound of the minimax ri
 sks is established.\nThe third one is related to the analysis of the so-ca
 lled Bayesian likelihood ratio. The multivariate density model on $R^d$ re
 quires development of the original technique.\n\nIn the second part of the
  talk I discuss  the application of  the proposed approach to the estima
 tion of $L_p$-norm of a density\, $1&lt\;p&lt\;infty$. The considered func
 tional class  is the intersection of usual $L_q$-ball\, $1&lt\;qleqinfty$
  with a ball in an arbitrary anisotropic Nikolskii semi-metric. Some unusu
 al phenomena related to the decay of minimax risk will be presented.
CATEGORIES:Séminaire,Statistique
END:VEVENT
BEGIN:VTIMEZONE
TZID:Europe/Paris
X-LIC-LOCATION:Europe/Paris
BEGIN:STANDARD
DTSTART:20211031T020000
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
END:STANDARD
END:VTIMEZONE
END:VCALENDAR