Convergence Characteristics of Methods of Regularization Estimators for Nonlinear Operator Equations

The paper studies convergence properties of method of regularization estimators of θ in the abstract nonlinear regression model \[ z_i = η (θ ;x_i ) + ε _i , i = 1,2, ⋯ ,\] where η (θ ;x) are nonlinear functionals of θ and the ε ᵢ’s are uncorrelated measurement errors with mean zero and bounded Variance. Convergence rates for method of regularization estimators are developed. The degree of nonlinearity of the operator η plays an important role in this analysis. The theory is illustrated with some applications to nonlinear integral equations and system identification.