Stochastic Estimation of the Maximum of a Regression Function

Let $M(x)$ be a regression function which has a maximum at the unknown point θ. 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 θ in probability as n → ∞.