Christophe Chesneau, Salima El Kolei, Junke Kou, Fabien Navarro
arXiv 18 Jun 2019 · Mathematics — Statistics Theory · publishedJournal of Computational and Applied Mathematics (2020) · 13 citations (OpenAlex)
arXiv:1906.07695 · PDF · DOI · OpenAlex · Extracted main text
In this paper, we consider an unknown functional estimation problem in a general nonparametric regression model with the feature of having both multiplicative and additive noise.We propose two new wavelet estimators in this general context. We prove that they achieve fast convergence rates under the mean integrated square error over Besov spaces. The obtained rates have the particularity of being established under weak conditions on the model. A numerical study in a context comparable to stochastic frontier estimation (with the difference that the boundary is not necessarily a production function) supports the theory.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Härdle, W., G. Kerkyacharian, D. Picard, and A. Tsybakov (2012) Wavelets, approximation, and statistical applications, Volume 129 | 1.000 | 6 | 3 | 100% |
| 2 | Delyon, B. and A. Juditsky (1996) On minimax wavelet estimators | 0.928 | 4 | 3 | 100% |
| 3 | Nason, G. P (1996) Wavelet shrinkage using cross-validation | 0.737 | 3 | 2 | 100% |
| 4 | Cai, T. T., L. Wang, et al (2008) Adaptive variance function estimation in heteroscedastic nonparametric regression | 0.644 | 2 | 2 | 100% |
| 5 | Chaubey, Y. P., C. Chesneau, and H. Doosti (2015) Adaptive wavelet estimation of a density from mixtures under multiplicative censoring | 0.644 | 2 | 2 | 100% |
| 6 | Chesneau, C (2013) On the adaptive wavelet estimation of a multidimensional regression function under $$-mixing dependence: Beyond the standard ass… self | 0.644 | 2 | 2 | 100% |
| 7 | Donoho, D. L., I. M. Johnstone, G. Kerkyacharian, and D. Picard (1995) Wavelet shrinkage: asymptopia? | 0.644 | 2 | 2 | 100% |
| 8 | Jirak, M., A. Meister, M. Rei, et al (2014) Adaptive function estimation in nonparametric regression with one-sided errors | 0.644 | 2 | 2 | 100% |
| 9 | Tsybakov, A. B (2009) Introduction to nonparametric estimation. revised and extended from the 2004 french original. translated by vladimir zaiats | 0.644 | 2 | 2 | 100% |
| 10 | Navarro, F. and A. Saumard (2017) Slope heuristics and v-fold model selection in heteroscedastic regression using strongly localized bases self | 0.585 | 3 | 1 | 100% |
Showing the top 10 of 47 scored citations.