Statistical inference for the optimal approximating model
In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (c...
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| Veröffentlicht in: | Probability theory and related fields 2013-04, Vol.155 (3-4), p.839-865 |
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| creator | Rohde, Angelika Dümbgen, Lutz |
| description | In the setting of high-dimensional linear models with Gaussian noise, we investigate the possibility of confidence statements connected to model selection. Although there exist numerous procedures for adaptive (point) estimation, the construction of adaptive confidence regions is severely limited (cf. Li in Ann Stat 17:1001–1008,
1989
). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral
χ
2
-distributions, we show that the risk and quadratic loss of all models within our confidence region are uniformly bounded by the minimal risk times a factor close to one. |
| doi_str_mv | 10.1007/s00440-012-0414-7 |
| format | Article |
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1989
). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral
χ
2
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1989
). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral
χ
2
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1989
). The present paper sheds new light on this gap. We develop exact and adaptive confidence regions for the best approximating model in terms of risk. One of our constructions is based on a multiscale procedure and a particular coupling argument. Utilizing exponential inequalities for noncentral
χ
2
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| source | Business Source Complete; Springer Nature - Complete Springer Journals |
| subjects | Adaptation Analysis Approximation Confidence Confidence intervals Construction Economics Finance Gaussian Generalized linear models Hypotheses Inequalities Insurance Management Mathematical and Computational Biology Mathematical and Computational Physics Mathematics Mathematics and Statistics Noise Normal distribution Operations Research/Decision Theory Optimization Probability Probability Theory and Stochastic Processes Quantitative Finance Random noise Risk Statistical inference Statistics for Business Studies Theoretical |
| title | Statistical inference for the optimal approximating model |
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