In this dissertation we develop a theory which offers a unified approach to the problem of obtaining stochastic versions of deterministic rearrangement inequalities. / To develop the theory we first define two new classes of functions and establish preservation properties of these functions under various statistical and mathematical operations. / Next we introduce the notion of stochastically similarly arranged (SSA) pairs of random vectors. We prove that if the random vectors (X,Y) are SSA and the function f from R('n) x R('n) into R('n) is monotone with respect to a certain partial ordering on R('n) x R('n) then for every permutation (pi) the stochastic inequalities / (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI) / hold. This result yields a unified way of obtaining stochastic versions of rearrangement inequalities. / We then show that many multivariate densities of interest in statistical practice govern pairs of random vectors which are SSA. / Next we show that under certain statistical operations on pairs of SSA random vectors the property of being SSA is preserved. For example, we show that the rank order of SSA random variables is SSA. We also show that the SSA property is preserved under certain contamination models. / Finally, we show how the results we obtain can be applied to problems in hypothesis testing. / Source: Dissertation Abstracts International, Volume: 42-10, Section: B, page: 4112. / Thesis (Ph.D.)--The Florida State University, 1981.
| Identifer | oai:union.ndltd.org:fsu.edu/oai:fsu.digital.flvc.org:fsu_74676 |
| Contributors | D'ABADIE, CATHERINE ANNE., Florida State University |
| Source Sets | Florida State University |
| Detected Language | English |
| Type | Text |
| Format | 82 p. |
| Rights | On campus use only. |
| Relation | Dissertation Abstracts International |
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