Estimation of the convergence rate for densities in the metric of Lp
β Scribed by J. Banys
- Publisher
- Springer
- Year
- 1976
- Tongue
- English
- Weight
- 193 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0363-1672
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π SIMILAR VOLUMES
We estimate the common density function of n i.i.d. observations, at a ΓΏxed point, over Sobolev classes of functions having regularity ΓΏ. We prove that the optimal rate of convergence cannot be attained in adaptive estimation, i.e. uniformly over ΓΏ in some interval B n. A slower rate is shown to be
The problem of estimating a density which is allowed to have discontinuities of the first kind is considered. The usual Fourier-type estimator is based on the Dirichlet or sinc kernel and is not suitable to eliminate the Gibbs phenomenon. Fourier4Ses~ro approximation yields the Fejrr kernel which is