nonlinear regression mode

Consistency of Least Squares Estimator of Linear Regression Parameter in Case of Discrete Tme and Long-Range or Weak Dependent Regressors

Linear regression model with discrete time, long-range/weak dependent random noise and time dependent regressors, which are observed with long L range/weak dependent errors, is considered. Parameter estimation of such models is one of the important problems of statistics of random processes. Least squares estimator is chosen for the estimation. The aim of the work is to prove consistency of least squares estimator of such regression model.

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.

Moments Asymptotic Expansion of the Least Squares Estimator of the Vector-Parameter of Nonlinear Regression with Correlated Observations

A nonlinear regression model with continuous time and mean square continuous separable measurable Gaussian stationary random noise with zero mean and integrable covariance function is considered. Parameter estimation in the models of such kind is an important problem of statistics of random processes. In this paper, the first terms of asymptotic expansions of the bias vector and covariance matrix of the least square estimator of nonlinear regression function vector parameter are obtained.