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 -