Asymptotic analysis of outliers dectection algorithms using a new empirical process result
<p>The Robustified Least Squares and the Impulse Indicator Saturation are iterative algorithms concerned with detecting outliers and other unsuspected structures in data. These two algorithms are constructed when the full or split sample least squares are chosen as the initial estimators for t...
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| Format: | Thesis |
| Language: | English |
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2015
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| Summary: | <p>The Robustified Least Squares and the Impulse Indicator Saturation are iterative algorithms concerned with detecting outliers and other unsuspected structures in data. These two algorithms are constructed when the full or split sample least squares are chosen as the initial estimators for the iterated 1-step Huber-skip M-estimator. These methods classify observations as outliers or not. This paper establishes an asymptotic theory considering the role of the varying cut-off in such algorithms. In particular, we demonstrate the tightness property for estimates in each iterated step with the varying cut-off. Moreover, a Poisson exceedence theory to the gauge is built for all iterations. The argument involves a theory for a new class of the weighted and marked empirical process.</p> |
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