An Upper Bound for the Number of Steps in Sequential Design

Summary

It is considered the sequential experimental designing in the problem of estimation of all unknown parameters of a linearized nonlinear regression model. The estimations are obtained by the method of least squares. As criterion of optimality the locally D ‐optimality is used.

The functional underlying this criterion is a functional of the information‐matrix which depends on the unknown parameters, i. e., it is, in general, not possible to determine a locally D ‐optimal experimental design before starting the experimentation. Therefore, a sequential procedure is used. Before starting this procedure the given size of observations is to be decomposed in a certain number q of partial sizes n ₁ , n ₂ , …, n _q . Then experimental designs are planned and realized stepwise with regard to n ₁ , n ₂ , …, n _q and all information about the unknown parameter vector just obtained. This means that the whole experiment is ( q – 1)‐times interrupted. Each interruption may be connected with an expense not negligible. Therefore, the choice of q depends, in general, on this expense too. In the following article we give an upper bound for the choice of q which depends from the expense of interruption and the size of the initial design only.