Prihodko V.V.

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.

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

We consider linear regression model with continuous time and strongly dependent stationary Gaussian random noise. The behavior of normalized in some way extreme residuals, that are the maximum differences, or their absolute values, between the observations and the values of the regression function where instead of unknown parameter the least squares estimator is substituted. For linear regression model the conditions of weak convergence of normalized extreme residuals to double exponent curve are obtained which follows from the assumption of normality of random noise.