On the Probability of Correct Selection when K is Large
- ISBN-10
- 0549694757
- ISBN-13
- 9780549694755
- Category
- Estimation theory
- Pages
- 240
- Language
- English
- Published
- 2008
- Author
- Jason Wilson
Description
Given k populations, it is often desirable to select the best t. The body of ranking and selection literature from 1954 to 1992 thoroughly addressed this problem for small k and small t. However, the advent of massive datasets has demanded further development. This dissertation focuses on the ranking and selection statistic called probability of correct selection (PCS), when k and t are large. It shows that when k is large, using the usual definition, PCS becomes too small to be useful. Three extensions of PCS are given. The first two are demonstrated to complement conventional methods of selection, such as multiple testing, by offering PCS as a measure of the quality of a particular selection. In this way, competing selections may be compared. The third extension is incorporated into an alternative method of selection. The performance of this method can be comparable to the best multiple testing methods. It has an advantage in that it requires one less pre-specified parameter, and it provides some additional information.
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