M-estimators in linear models with long range dependent errors. (English) Zbl 0759.62023
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.
Reviewer: M.Huzii (Tokyo)
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 62F12 | Asymptotic properties of parametric estimators |
Keywords:
dependent errors; skew symmetric scores; symmetric errors; least squares estimator; asymptotic normality; non-normality; Hermite rank; polynomials; linearity; linear model; stationary mean zero random vector process; Gaussian process; long range dependence; \(M\)-estimator; non- random designsReferences:
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