Two-stage adaptive optimal design with fixed first-stage sample size
type: Item
instance of: scholarly article
title: Two-stage adaptive optimal design with fixed first-stage sample size
zbMATH Open document ID: 1263.62107
DOI: 10.1155/2012/436239
author: Adam Lane
author: Nancy Flournoy
published in: Journal of Probability and Statistics
publication date: 2012-10-10T00:00:00Z
review text: Summary: 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 a 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.
Mathematics Subject Classification ID: 62L05
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62F12
Mathematics Subject Classification ID: 65C60
zbMATH DE Number: 6092410
Wikidata QID: Q58910962
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/436239
OpenAlex ID: W2039871288
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description: scientific article; zbMATH DE number 6092410