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CATEGORIES:Statistics
SUMMARY:Robust density estimation and model selection for
the L1 loss : Applications to shape-constrained de
nsity estimation. - Hélène Halconruy (Télécom SudP
aris)
DTSTART;TZID=Europe/London:20240209T140000
DTEND;TZID=Europe/London:20240209T150000
UID:TALK209548AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209548
DESCRIPTION:There is a growing interest in shape-constrained m
ethods in the field of statistical inference. The
idea is to replace restrictive parametric assumpti
ons about the target function (here a density) wit
h a shape constraint that it must satisfy such as
convexity\, monotonicity\, and log-concavity. The
favourite estimator used in this framework is the
maximum likelihood estimator (MLE) which shows goo
d adaptation properties with respect to some speci
fic classes of densities and reaches optimal globa
l\nconvergence rates.\n\nIn a first joint work wit
h Y. Baraud and G. Maillard\, we design\, in the o
ne-dimensional case\, a general estimation procedu
re for the L1-loss that retains the minimax and ad
aptation properties of the MLE and that is also ro
bust: it remains stable with respect to a slight d
eviation from an ideal situation where the data ar
e truly i.i.d. and their density belongs to the mo
del under consideration.\nIn this talk\, I will pr
esent the density estimator and a model selection
procedure that we are currently working on. I will
illustrate both on density models where the densi
ty satisfies some shape constraint such (piecewise
) monotonicity and (piecewise) convex/concavity.
LOCATION:MR12\, Centre for Mathematical Sciences
CONTACT:Dr Sergio Bacallado
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