Estimation in ill-posed linear models with nuisance design
| Autor: | Thomas Zimolo, Yuri Golubev |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Marseille (I2M), Aix Marseille Université (AMU)-École Centrale de Marseille (ECM)-Centre National de la Recherche Scientifique (CNRS), Université de Provence - Aix-Marseille 1, Centre National de la Recherche Scientifique (CNRS)-École Centrale de Marseille (ECM)-Aix Marseille Université (AMU) |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Mean square Well-posed problem Mathematical optimization noisy deconvolution Primary 62C99 secondary 62C10 62C20 62J05 Gaussian Linear model secondary 62C10 Minimax inverse minimax estimation [STAT]Statistics [stat] Combinatorics symbols.namesake roughness penalty approach Regularization (physics) symbols Van Trees inequality Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Mathematical Methods of Statistics Mathematical Methods of Statistics, 2015, 24 (1), ⟨10.3103/S1066530715010019⟩ Mathematical Methods of Statistics, Allerton Press, Springer (link), 2015, 24 (1), ⟨10.3103/S1066530715010019⟩ |
| ISSN: | 1934-8045 1066-5307 |
| DOI: | 10.3103/s1066530715010019 |
| Popis: | International audience; The paper deals with recovering an unknown vector θ ∈ Rp in two simple linear models: in the first one we observe y = b · θ + ξ and z = b + σξ , whereas in the second one we have at our disposal y' = b^2 · θ + ∈b · ξ and z = b + σξ'. Here b ∈ R^p is a nuisance vector with positive components and ξ, ξ' ∈ R^p are standard white Gaussian noises in R^p. It is assumed that p is large and components bk of b are small for large k. In order to get good statistical estimates of θ in this situation, we propose to combine minimax estimates of 1/bk and 1/b^2k with regularization techniques based on the roughness penalty approach. We provide new non-asymptotic upper bounds for the mean square risks of the estimates related to this method. |
| Databáze: | OpenAIRE |
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