Robust location estimation under dependence

Abstract

We discuss the approximation of the mean of autocorrelated data under contaminations of different types. Many robust location estimators have been investigated carefully for independent data, but their properties have not been studied in detail under dependencies. We pay attention to estimators based on subranges like minimum volume ellipsoid and minimum covariance determinant estimators, mid-ranges and trimmed means, of which the sample mean and median are special cases, and also include the Hodges–Lehmann and the Bickel–Hodges estimators. Our interest is in small to moderate sample sizes.

Keywords:

• Time series
• Robustness
• Additive outliers
• Innovative outliers
• Sensitivity function
• Bias curve

Acknowledgements

The comments of the referee are gratefully acknowledged.

Additional information

Notes on contributors

Roland Fried

Email: [email protected]