TY - JOUR
A2 - Chen, Zhengjia
AU - Lane, Adam
AU - Flournoy, Nancy
PY - 2012
DA - 2012/10/04
TI - Two-Stage Adaptive Optimal Design with Fixed First-Stage Sample Size
SP - 436239
VL - 2012
AB - 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.
SN - 1687-952X
UR - https://doi.org/10.1155/2012/436239
DO - 10.1155/2012/436239
JF - Journal of Probability and Statistics
PB - Hindawi Publishing Corporation
KW -
ER -