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UID:8417@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20140328T110000
DTEND;TZID=Europe/Paris:20140328T120000
DTSTAMP:20241120T210407Z
URL:https://www.i2m.univ-amu.fr/evenements/hyperbolic-wavelet-based-method
 s-in-nonparametric-function-estimation-and-hypothesis-testing-jean-marc-fr
 eyermuth/
SUMMARY:Jean-Marc Freyermuth (KU Leuven\, Belgium): Hyperbolic wavelet-base
 d methods in nonparametric function estimation and hypothesis testing - Je
 an-Marc Freyermuth
DESCRIPTION:Jean-Marc Freyermuth: In this talk we are interested in nonpara
 metric multivariate function estimation. In Autin et al. (2013\, 2014a)\, 
 we determine the maxisets of several estimators based on thresholding of t
 he empirical hyperbolic wavelet coefficients. That is we determine the lar
 gest functional space over which the risk of these estimators converges at
  a chosen rate. It is known from the univari- ate setting that pooling inf
 ormation from geometric structures (horizontal/vertical blocks) in the coe
 fficient domain allows to get ’large’ maxisets (see e.g Autin et al.\,
  2011\, 2012\, 2014b). In the multidimensional setting\, the situation is 
 less straightforward. In a sense these estimators are much more exposed to
  the curse of dimensionality. However we identify cases where infor- matio
 n pooling has a clear benefit. In particular\, we identify some general st
 ructural constraints that can be related to compound models and to a ’mi
 nimal’ level of anisotropy. If time allows we will also discuss either t
 he application of such methods for estimating the time-frequency spec- tru
 m of a (zero mean) non-stationary time series with second order structure 
 which varies across time (in the spirit of (Neumann and von Sachs\, 1997))
 \; or how the geometry of the hyperbolic wavelet basis allows to construct
  ’optimal’ testing procedures of some structural characteristics of th
 e estimand.\n\nhttps://www.econ.kuleuven.be\n&nbsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Jean-Marc_Freyermuth.jpg
CATEGORIES:Séminaire,Probabilités
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