Expansion estimation by Bayes rules |
| |
| Institution: | 1. Institute of Statistics and Decision Sciences, Old Chem Building, Duke University, Box 90251, Durham, NC 27708-0251, USA;2. Consiglio Nazionale delle Ricerche, Istituto per le Applicazioni, della Matematica e dell''Informatica, Via A. M. Ampere, 56 I-20131 Milano, Italy;1. Department of Computing Science, University of Alberta, Edmonton, Canada;2. Information Systems Engineering, Ben Gurion University, Beer-Sheva, 85104, Israel;3. Department of Computer Science, University of Texas at Austin, Austin, TX, USA;4. Department of Computer Science, University of Denver, Denver, CO, USA |
| |
| Abstract: | In the problem of estimating a location parameter in any symmetric unimodal location parameter model, we demonstrate that Bayes rules with respect to squared error loss can be expanders for some priors that belong to the family of all symmetric priors. That generalizes the results obtained by DasGupta and Rubin for the one dimensional case. We also consider symmetric priors which either have an appropriate point mass at 0 or are unimodal, and prove that under the latter condition all Bayes rules are shrinkers. Results of such nature are important, for example, in wavelet based function estimation and data denoising, where shrinkage of wavelet coefficients is associated with smoothing the data. We illustrate the results using FIAT stock market data. |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
