Premium
Non‐parametric Estimation of the Death Rate in Branching Diffusions
Author(s) -
HÖPFNER R.,
HOFFMANN M.,
LÖCHERBACH E.
Publication year - 2002
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/1467-9469.00312
Subject(s) - mathematics , branching process , minimax , estimator , particle system , ergodicity , rate of convergence , parametric statistics , statistical physics , mathematical analysis , combinatorics , statistics , mathematical optimization , channel (broadcasting) , physics , computer science , electrical engineering , engineering , operating system
We consider finite systems of diffusing particles in with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position‐dependent branching rate based on the observation of the particle process over a time interval [0, t ]. Asymptotics are taken as t → ∞. We introduce a kernel‐type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared‐error loss over a range of Hölder classes and show that our estimator is asymptotically optimal.