M-estimators in linear models with long range dependent errors
The author considers the linear model \(Y_ i=X_ i'\beta+\varepsilon_ i\), where \(\{Y_ i\}\) is an observable process, \(X_ i'=(1,\xi_ i')\), is an observable \(p\times 1\) stationary mean zero random vector process, \(\beta\) is an unknown constant vector and \(\{\varepsilon_ i\}\) is a measurable transformation of a strictly stationary mean zero, unit variance Gaussian process \(\{\eta_ i\}\). He assumes long range dependence of \(\{\xi_ i\}\) and \(\{\eta_ i\}\) and considers an \(M\)- estimator \(\hat\beta_ N\) of \(\beta\). Under some conditions, he evaluates the asymptotic behavior of \(\hat\beta_ N-\beta\) and shows some formulas concerning asymptotics. The case of non-random designs is also mentioned.
stationary mean zero random vector process
scientific article; zbMATH DE number 93348
scientific article