Strong Uniform Convergence Rates of Wavelet Density Estimators with Size-Biased Data
This paper considers the strong uniform convergence of multivariate density estimators in Besov space Bp,qs(Rd) based on size-biased data. We provide convergence rates of wavelet estimators when the parametric μ is known or unknown, respectively. It turns out that the convergence rates coincide with...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/7102346 |
| Summary: | This paper considers the strong uniform convergence of multivariate density estimators in Besov space Bp,qs(Rd) based on size-biased data. We provide convergence rates of wavelet estimators when the parametric μ is known or unknown, respectively. It turns out that the convergence rates coincide with that of Giné and Nickl’s (Uniform Limit Theorems for Wavelet Density Estimators, Ann. Probab., 37(4), 1605-1646, 2009), when the dimension d=1, p=q=∞, and ω(y)≡1. |
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| ISSN: | 2314-8896 2314-8888 |