Adaptive sequential estimation for ergodic diffusion processes in quadratic metric

作者：Galtchouk L I^*; Pergamenshchikov S M

来源：Journal of Nonparametric Statistics, 2011, 23(2): 255-285.

DOI：10.1080/10485252.2010.544307

• adaptive nonparametric estimation
• non-asymptotic estimation
• model selection
• sharp oracle inequality
• quadratic risk
• sequential estimation
• asymptotic bounds
• efficient estimation

An adaptive nonparametric procedure is constructed for estimating the unknown drift coefficient in ergodic diffusion processes. A sharp non-asymptotic upper bound (an oracle inequality) is obtained for a quadratic risk. Furthermore, an asymptotic lower bound for the minimax quadratic risk is found that equals to the Pinsker constant. Asymptotic efficiency is proved, that is, the asymptotic quadratic risk of the constructed estimator coincides with this constant.

• 出版日期2011