統計的検定法の見地からのニュートン法の修正

The Newton method has quitely universal use for a nonlinear optimization problem,max{ f(x) : x ∈U } . The algorithm satisfies to be quadratically convergent under a mildcondition. This paper concentrates on the further convergence from a statistical viewpoint.A deformation of the objective function f is proposed by association with methods of statisticaltesting hypothesis. It is shown that the k-step modified function enjoys convergence of(k + 2)-th order.