Data-driven wavelet estimations in the convolution structure density model

Kaikai Cao; Kaikai Cao

doi:10.3934/math.2024829

AIMS Mathematics

2024, Volume 9, Issue 7: 17076-17088. doi: 10.3934/math.2024829

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Data-driven wavelet estimations in the convolution structure density model

Kaikai Cao ^,

School of Mathematics and Statistics, Weifang University, Weifang 261061, China

Received: 13 March 2024 Revised: 06 May 2024 Accepted: 08 May 2024 Published: 16 May 2024
MSC : 42C40, 62G07, 62G20

Based on a data-driven kernel estimator, Lepski and Willer considered the problem of adaptive $ L^{p} $ risk estimations in the convolution structure density model in 2017 and 2019. This current paper studies the same problem with a data-driven wavelet estimator on Besov spaces, as wavelet estimations offer fast algorithm and provide more local information. Our results can reduce to the traditional adaptive wavelet estimations in the classical density model with no errors, as well as deconvolutional model.
- wavelets,
- Besov spaces,
- density estimations,
- generalized deconvolution model,
- adaptivity
Citation: Kaikai Cao. Data-driven wavelet estimations in the convolution structure density model[J]. AIMS Mathematics, 2024, 9(7): 17076-17088. doi: 10.3934/math.2024829

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Abstract

Based on a data-driven kernel estimator, Lepski and Willer considered the problem of adaptive $ L^{p} $ risk estimations in the convolution structure density model in 2017 and 2019. This current paper studies the same problem with a data-driven wavelet estimator on Besov spaces, as wavelet estimations offer fast algorithm and provide more local information. Our results can reduce to the traditional adaptive wavelet estimations in the classical density model with no errors, as well as deconvolutional model.

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