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On confidence intervals for distribution function and density of ergodic diffusion process

✍ Scribed by D. Dehay; Yu.A. Kutoyants

Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
228 KB
Volume
124
Category
Article
ISSN
0378-3758

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✦ Synopsis

In the problems of invariant distribution and density estimation of an ergodic di usion process, the asymptotic variances of many estimators can be represented as some mathematical expectations with respect to the invariant law. Therefore, the construction of the conÿdence intervals requires the estimates of these quantities. The present work proposes estimators of them which are consistent and so it allows to construct the corresponding conÿdence intervals. Moreover, these quantities play an important role in the problems of asymptotically e cient estimation of the distribution function and density.

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On efficient estimation of invariant density for ergodic diffusion processes
✍ Ilia Negri 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 96 KB

The problem of nonparametric invariant density function estimation of an ergodic di usion process is considered. The local asymptotic minimax lower bound on the risk of all the estimators is established. The asymptotic risk considered measures the distance between the estimators and the density that