Up-and-Down and the Percentile-Finding Problem
| dc.creator | Oron, Assaf P. | |
| dc.date | 2008-08-21 | |
| dc.date.accessioned | 2026-07-07T09:57:54Z | |
| dc.date.available | 2026-07-07T09:57:54Z | |
| dc.description | Up-and-Down (U&D) is a popular sequential design for estimating threshold percentiles in binary experiments. However, U&D application practices have stagnated, and significant gaps in understanding its properties persist. The first part of my work aims to fill gaps in U&D theory. New results concerning stationary distribution properties are proven. A second focus of this study is nonparametric U&D estimation. An improvement to isotonic regression called "centered isotonic regression" (CIR), and a new averaging estimator called "auto-detect" are introduced and their properties studied. Bayesian percentile-finding designs, most notably the continual reassessment method (CRM) developed for Phase I clinical trials, are also studied. In general, CRM convergence depends upon random run-time conditions -- meaning that convergence is not always assured. Small-sample behavior is studied as well. It is shown that CRM is quite sensitive to outlier sub-sequences of thresholds, resulting in highly variable small-sample behavior between runs under identical conditions. Nonparametric CRM variants exhibit a similar sensitivity. Ideas to combine the advantages of U&D and Bayesian designs are examined. A new approach is developed, using a hybrid framework, that evaluates the evidence for overriding the U&D allocation with a Bayesian one. | |
| dc.description | This is the full text of my Ph.D. dissertation as accepted at the University of Washington in Fall 2007. Further improvements should be available shortly in peer-reviewed articles. The dissertation is posted here "as is" for public access. See also R package "cir" for an implementation of the improved isotonic-regression estimator | |
| dc.identifier | https://arxiv.org/abs/0808.3004 | |
| dc.identifier | http://arxiv.org/abs/0808.3004 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167516 | |
| dc.subject | Methodology | |
| dc.subject | Statistics Theory | |
| dc.title | Up-and-Down and the Percentile-Finding Problem | |
| dc.type | text |