maximal residuals

The Limit Theorems for Extreme Residuals in Nonlinear Regression Model with Gaussian Stationary Noise

In this paper non-linear regression model with Gaussian stationary random noise and continuous time is considered. The behavior of normalized in some way maximum residuals and maximum of residuals absolute values in which its the least squares estimator is substituted instead of unknown parameter of regression function. The convergence of distribution of these normalized maximum to double exponent law is proved which follows from the assumption of random noise normality.