Replicationfree optimal design in regression analysis (Q1298198)

The paper deals with the optimal choice of the design points in analysis of the nonlinear regression model \(y_i=f(x_i,\theta)+e_i\), \(i=1,\dots,n\), \(x_i\in B=\{x_1,\dots,x_N\}\), where the errors \(e_i\) are i.i.d.r.v. and the unknown parameter \(\theta\) may posses \(p\leq n<N\) components. The design is said to be replication-free if each design point is used only once. The determination of an optimal replication-free design (ORD) implies the generation and evaluation of all possible \({N\choose n}\) designs, that is why the problem of quick enumeration becomes very important. The authors discuss quick enumeration algorithms such as ``straightforward'', ``tree algorithm'' and ``complete tree algorithm'' for exact ORD as well as a number of search algorithms, which give the good approximation of the optimal designs. Their performances are illustrated by some examples.