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SUMMARY:Robust density estimation and model selection for the L1 loss : Ap
 plications to shape-constrained density estimation. - Hélène Halconruy (
 Télécom SudParis)
DTSTART:20240209T140000Z
DTEND:20240209T150000Z
UID:TALK209548@talks.cam.ac.uk
CONTACT:Dr Sergio Bacallado
DESCRIPTION:There is a growing interest in shape-constrained methods in th
 e field of statistical inference. The idea is to replace restrictive param
 etric assumptions about the target function (here a density) with 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 good adaptation properties with res
 pect to some specific classes of densities and reaches optimal global\ncon
 vergence rates.\n\nIn a first joint work with Y. Baraud and G. Maillard\, 
 we design\, in the one-dimensional case\, a general estimation procedure f
 or the L1-loss that retains the minimax and adaptation properties of the M
 LE and that is also robust: it remains stable with respect to a slight dev
 iation from an ideal situation where the data are truly i.i.d. and their d
 ensity belongs to the model under consideration.\nIn this talk\, I will pr
 esent the density estimator and a model selection procedure that we are cu
 rrently working on. I will illustrate both on density models where the den
 sity satisfies some shape constraint such (piecewise) monotonicity and (pi
 ecewise) convex/concavity.
LOCATION:MR12\, Centre for Mathematical Sciences
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