On fixed-precision estimation of the minimum of a regression function and of the minimum of a random variable

The problem of sequential fixed-precision estimation of the minimum point of a quadratic regression function is investigated. Stochastic approximation methods are mentioned. One presents also some sequential fixed-precision procedures for the minimum of a random variable, i.e. for the lower bound of the support of its distribution function. One attempts to apply these procedures to estimation of the minimal value of a regression function. Asymptotically consistent fixed-precision estimation is considered.