Outlier detection and trimmed estimation in general functional spaces

Details Outlier detection and trimmed estimation in general functional spaces Outlier detection and trimmed estimation in general functional spaces

2010-01-07

arxiv.org/abs/1001.1014v1

Statistics

Methodology

Scientific paper

This article introduces trimmed estimators for the mean and covariance functional of data in general Hilbert spaces. The estimators are based on a data depth measure that can be computed on any Hilbert space, because it is defined only in terms of the interdistances between data points. We show that the estimators can attain the maximum breakdown point by properly choosing the tuning parameters, and that they possess better outlier resistance properties than alternative estimators, as shown by a comparative Monte Carlo study. The data depth measure we introduce can also be used for visual screening of the data and is a practical tool to detect clusters and isolated outliers, as shown by three real-data applications.

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