On the exactness of normal approximation of LSE of regression coefficient of long-memory random fields (Q1573636)

The authors study the regression model \(\zeta(x) =\theta g(x)+ \eta(x)\), \(x\in\Delta (T)\subseteq R^n\), where \(\eta(x)= G(\xi(x))\) and \(\xi(x)\) is a homogeneous Gaussian field. The correlation function of \(\xi(x)\) is supposed to be a regularly varying function with exponent \(-\alpha\). The authors establish the exact rate of convergence to the standard normal distribution of the distribution of the suitably standardized least squares estimator \(\widehat \theta_T\).