A sequential design for estimating a nonlinear parametric function

摘要

A fully-sequential design for estimating a nonlinear function of the parameters in the simple linear regression model is proposed and its asymptotic behavior is investigated both theoretically and by simulation. The design requires that the observations be taken at x=±1 and specifies whether the next observation is to be taken at x=−1 or 1. It is shown that, under this design, the mean number of observations taken at x=1, mk, converges with probability one to an optimal value as k→∞, where k denotes the total number of design points. The simulation study indicates that mk converges in L2 to the optimal value with the order of O(k−2).