Tikhonov–Phillips regularizations in linear models with blurred design
| Autor: | Yu. Golubev, Th. Zimolo |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Pure mathematics Mathematical optimization Gaussian 05 social sciences 01 natural sciences Noise (electronics) Regularization (mathematics) Tikhonov regularization 010104 statistics & probability symbols.namesake Additive white Gaussian noise 0502 economics and business symbols 0101 mathematics Statistics Probability and Uncertainty Concentration inequality Condition number 050205 econometrics P-matrix Mathematics |
| Zdroj: | Mathematical Methods of Statistics. 25:1-25 |
| ISSN: | 1934-8045 1066-5307 |
| DOI: | 10.3103/s1066530716010014 |
| Popis: | The paper deals with recovering an unknown vector β ∈ ℝ p based on the observations Y = Xβ + є ξ and Z = X + σζ, where X is an unknown n × p matrix with n ≥ p, ξ ∈ ℝ p is a standard white Gaussian noise, ζ is an n × p matrix with i.i.d. standard Gaussian entries, and є, σ ∈ ℝ+ are known noise levels. It is assumed that X has a large condition number and p is large. Therefore, in order to estimate β, the simple Tikhonov–Phillips regularization (ridge regression) with a data-driven regularization parameter is used. For this estimation method, we study the effect of noise σζ on the quality of recovering Xβ using concentration inequalities for the prediction error. |
| Databáze: | OpenAIRE |
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