Simultaneous estimation by isotonic regression

✍ Scribed by M.A. Fernández; C. Rueda; B. Salvador

• Book ID: 104340536
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 390 KB
• Volume: 70
• Category: Article
• ISSN: 0378-3758
• DOI: 10.1016/s0378-3758(97)00183-3

✦ Synopsis

We consider a random vector X with unimodal density, diagonal covariance matrix, f2-~, and location parameter 0 subject to order restrictions. For this model the maximum likelihood estimator (MLE) X* is the so-called isotonic regression. It is well known that, in certain situations, X* is not better than X when coordinate estimation is considered. We focus on the comparison between the simultaneous constant length confidence intervals for the coordinates centered at X or at X*. We characterize situations where the coverage probability of the intervals is greater if X* is used instead of X. Special attention is given to the elliptically symmetric distributions with a total ordering or a tree ordering on 0.