\(S\)-estimation in the linear regression model with long-memory error terms under trend (Q2740040)

The linear regression model NEWLINE\[NEWLINEy_{i}(n)=x_{ii}(n)^{T}\theta(n)+e_{i}(n)NEWLINE\]NEWLINE is considered for \(i=1,\dots,n,\) where \(y_{i}(n)\) is the dependent variable, \(x_{i}(n)\) is a \(p\)-dimensional vector of fixed regressors, \(\theta(n)\) is the \(p\)-dimensional parameter vector and \(e_{i}(n)\) is an error process. Here, the case of a long-memory stationary process \(e_{i}(n)\) is considered. The asymptotic distribution of \(S\)-estimators is obtained under mild regularity conditions on the regressors which are sufficiently weak to cover, for example, polynomial trends and i.i.d. carriers. The \(S\)-estimators are asymptotically normal in the case of deterministic regressors with a variance-covariance structure similar to the structure in the i.i.d. case. The rate of convergence for \(S\)-estimators is the same as for the least-squares estimator and the best linear unbiased estimator.