The shrinkage estimation has proven to be very useful when dealing with a large number of mean parameters. In this dissertation, we consider the problem of simultaneous estimation of multiple variances and construct a shrinkage type, non-parametric estimator. We take the non-parametric empirical Bayes approach by starting with an arbitrary prior on the variances. Under an invariant loss function, the resultant Bayes estimator relies on the marginal cumulative distribution function of the sample variances. Replacing the marginal cdf by the empirical distribution function, we obtain a Non-parametric Empirical Bayes estimator for multiple Variances (NEBV). The proposed estimator converges to the corresponding Bayes version uniformly over a large set. Consequently, the NEBV works well in a post-selection setting. We then apply the NEBV to construct condence intervals for mean parameters in a post-selection setting. It is shown that the intervals based on the NEBV are shortest among all the intervals which guarantee a desired coverage probability. Through real data analysis, we have further shown that the NEBV based intervals lead to the smallest number of discordances, a desirable property when we are faced with the current "replication crisis". / Statistics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/3153 |
| Date | January 2018 |
| Creators | KWON, YEIL |
| Contributors | Zhao, Zhigen, Sarkar, S. K. (Sanat K.), Tang, Cheng Yong, Qiu, Jing |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 75 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/3135, Theses and Dissertations |
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