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SUMMARY:Nonparametric estimation of the division rate of a size-structured
  population - Vincent Rivoirard\, Université Paris-Dauphine
DTSTART:20120217T160000Z
DTEND:20120217T170000Z
UID:TALK35201@talks.cam.ac.uk
CONTACT:Richard Samworth
DESCRIPTION:We consider the problem of estimating the\ndivision rate of a 
 size-structured population in a\nnonparametric setting. The size of the sy
 stem evolves\naccording to a transport-fragmentation equation: each\nindiv
 idual grows with a given transport rate\, and splits\ninto two offsprings 
 of the same size\, following\na binary fragmentation process with unknown 
 division rate\nthat depends on its size. In contrast to a deterministic\ni
 nverse problem approach\, we take in this paper the\nperspective of statis
 tical inference: our data consists in\na large sample of the size of indiv
 iduals\, when the\nevolution of the system is close to its time-asymptotic
 \nbehavior\, so that it can be related to the eigenproblem of\nthe conside
 red transport-fragmentation equation. By\nestimating statistically each te
 rm of the eigenvalue\nproblem and by suitably inverting a certain linear\n
 operator\, we are able to construct a more realistic\nestimator of the div
 ision rate that achieves the same\noptimal error bound as in related deter
 ministic inverse\nproblems. Our procedure relies on kernel methods with\na
 utomatic bandwidth selection.
LOCATION:MR12\, CMS\, Wilberforce Road\, Cambridge\, CB3 0WB
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