Stochastic Estimation of the Maximum of a Regression Function

Let M (x) be a regression function which has a maximum at the unknown point. M (x) is itself unknown to the statistician who, however, can take observations at any level x. This paper gives a scheme whereby, starting from an arbitrary point x₁, one obtains successively x₂, x₃, such that xₙ converges to in probability as n.