Adaptive design in regression and control.

When y = M(x) + epsilon, where M may be nonlinear, adaptive regression designs of the levels x(1), x(2),... at which y(1), y(2),... are observed lead to asymptotically efficient estimates of the value theta of x for which M(theta) is equal to any desired value y(*). More importantly, these designs also make the "cost" of the observations, defined at the nth stage to be Sigma(1) (n) (x(i) - theta)(2), to be of the order of log n instead of n, an obvious advantage in medical and other applications.