Report
On optimality of Bayesian testimation in the normal means problem
| العنوان: | On optimality of Bayesian testimation in the normal means problem |
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| المؤلفون: | Abramovich, Felix, Grinshtein, Vadim, Pensky, Marianna |
| المصدر: | Annals of Statistics 2007, Vol. 35, No. 5, 2261-2286 |
| سنة النشر: | 2007 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Statistics Theory, 62C10 (Primary), 62C20, 62G05 (Secondary) |
| الوصف: | We consider a problem of recovering a high-dimensional vector $\mu$ observed in white noise, where the unknown vector $\mu$ is assumed to be sparse. The objective of the paper is to develop a Bayesian formalism which gives rise to a family of $l_0$-type penalties. The penalties are associated with various choices of the prior distributions $\pi_n(\cdot)$ on the number of nonzero entries of $\mu$ and, hence, are easy to interpret. The resulting Bayesian estimators lead to a general thresholding rule which accommodates many of the known thresholding and model selection procedures as particular cases corresponding to specific choices of $\pi_n(\cdot)$. Furthermore, they achieve optimality in a rather general setting under very mild conditions on the prior. We also specify the class of priors $\pi_n(\cdot)$ for which the resulting estimator is adaptively optimal (in the minimax sense) for a wide range of sparse sequences and consider several examples of such priors. Comment: Published in at http://dx.doi.org/10.1214/009053607000000226 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1214/009053607000000226 |
| URL الوصول: | http://arxiv.org/abs/0712.0904 |
| رقم الانضمام: | edsarx.0712.0904 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1214/009053607000000226 |
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