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Non‐parametric Kernel Estimation of the Coefficient of a Diffusion
Author(s) -
Jacod Jean
Publication year - 2000
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 - 10.1111/1467-9469.00180
Subject(s) - mathematics , pointwise , kernel density estimation , estimator , diffusion , kernel (algebra) , parametric statistics , kernel smoother , variable kernel density estimation , diffusion process , mathematical analysis , statistics , kernel method , combinatorics , physics , thermodynamics , knowledge management , innovation diffusion , artificial intelligence , radial basis function kernel , support vector machine , computer science
In this work we exhibit a non‐parametric estimator of kernel type, for the diffusion coefficient when one observes a one‐dimensional diffusion process at times i / n for i = , ..., n and study its asymptotics as n ←∞. When the diffusion coefficient has regularity r ≥ 1, we obtain a rate 1/ n r /(1+2 r ) , both for pointwise estimation and for estimation on a compact subset of R: this is the same rate as for non‐parametric estimation of a density with i.i.d. observations.