Orlovsky I.V.

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.

Asymptotic Properties of Estimator of Linear Regression Parameter in Case of Long-Range Dependent Regressors

The paper considers linear regression model with long-range/weak dependent random noise and time dependent regressors which are observed with long-range dependent errors. Parameter estimation of these models is an important problem of statistics of random processes. We choose widely used least squares estimator for the estimation. The aim of this work is to prove consistency and asymptotic normality of least squares estimator of the regression model.

On the unique M-estimates of nonlinear regression model parameters

Through experiments conducted, we uncover the conditions, under which M-estimate of the model parameter in the nonlinear regression model with continuous time and strong/weak dependent random noise is a unique solution of the system (in a definite asymptotic sense).