Asymptotic Confidence Regions for High-dimensional Structured Sparsity
| Autor: | Sara van de Geer, Benjamin Stucky |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Pointwise
Normalization (statistics) FOS: Computer and information sciences Matrix norm Estimator Machine Learning (stat.ML) Mathematics - Statistics Theory High dimensional Statistics Theory (math.ST) 010501 environmental sciences 01 natural sciences Nonzero coefficients 010104 statistics & probability Statistics - Machine Learning Signal Processing Linear regression FOS: Mathematics Applied mathematics 0101 mathematics Electrical and Electronic Engineering 0105 earth and related environmental sciences Mathematics |
| Popis: | In the setting of high-dimensional linear regression models, we propose two frameworks for constructing pointwise and group confidence sets for penalized estimators which incorporate prior knowledge about the organization of the non-zero coefficients. This is done by desparsifying the estimator as in van de Geer et al. [18] and van de Geer and Stucky [17], then using an appropriate estimator for the precision matrix $\Theta$. In order to estimate the precision matrix a corresponding structured matrix norm penalty has to be introduced. After normalization the result is an asymptotic pivot. The asymptotic behavior is studied and simulations are added to study the differences between the two schemes. Comment: 28 pages, 4 figures, 1 table |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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