Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size
In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are straightforward if one assumes the sample size of each stage goes to infinity with the overall sample size. However...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Probability and Statistics |
| Online Access: | http://dx.doi.org/10.1155/2012/436239 |
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| _version_ | 1832555814578028544 |
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| author | Adam Lane Nancy Flournoy |
| author_facet | Adam Lane Nancy Flournoy |
| author_sort | Adam Lane |
| collection | DOAJ |
| description | In adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are straightforward if one assumes the sample size of each stage goes to infinity with the overall sample size. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experiment. We study the large sample behavior of such studies. For simplicity, we assume a nonlinear regression model with normal errors. We show that the distribution of the maximum likelihood estimates converges to a scale mixture family of normal random variables. Then, for a one parameter exponential mean function we derive the asymptotic distribution of the maximum likelihood estimate explicitly and present a simulation to compare the characteristics of this asymptotic distribution with some commonly used alternatives. |
| format | Article |
| id | doaj-art-d2df0e2c10cd4870819bc4abc255b778 |
| institution | Kabale University |
| issn | 1687-952X 1687-9538 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Probability and Statistics |
| spelling | doaj-art-d2df0e2c10cd4870819bc4abc255b7782025-02-03T05:47:15ZengWileyJournal of Probability and Statistics1687-952X1687-95382012-01-01201210.1155/2012/436239436239Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample SizeAdam Lane0Nancy Flournoy1Department of Statistics, University of Missouri, 146 Middlebush Hall, Columbia, MO 65203, USADepartment of Statistics, University of Missouri, 146 Middlebush Hall, Columbia, MO 65203, USAIn adaptive optimal procedures, the design at each stage is an estimate of the optimal design based on all previous data. Asymptotics for regular models with fixed number of stages are straightforward if one assumes the sample size of each stage goes to infinity with the overall sample size. However, it is not uncommon for a small pilot study of fixed size to be followed by a much larger experiment. We study the large sample behavior of such studies. For simplicity, we assume a nonlinear regression model with normal errors. We show that the distribution of the maximum likelihood estimates converges to a scale mixture family of normal random variables. Then, for a one parameter exponential mean function we derive the asymptotic distribution of the maximum likelihood estimate explicitly and present a simulation to compare the characteristics of this asymptotic distribution with some commonly used alternatives.http://dx.doi.org/10.1155/2012/436239 |
| spellingShingle | Adam Lane Nancy Flournoy Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size Journal of Probability and Statistics |
| title | Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size |
| title_full | Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size |
| title_fullStr | Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size |
| title_full_unstemmed | Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size |
| title_short | Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size |
| title_sort | two stage adaptive optimal design with fixed first stage sample size |
| url | http://dx.doi.org/10.1155/2012/436239 |
| work_keys_str_mv | AT adamlane twostageadaptiveoptimaldesignwithfixedfirststagesamplesize AT nancyflournoy twostageadaptiveoptimaldesignwithfixedfirststagesamplesize |