Robust regression and outlier detection
Robust regression and outlier detection
Computational Statistics & Data Analysis
On a fast, robust estimator of the mode: Comparisons to other robust estimators with applications
Computational Statistics & Data Analysis
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Measures of location based on the shortest half sample, including the shorth and the location of the least median of squares, are more robust than the median to outliers, but less robust to contamination near the location. Although such measures can estimate the mode, the proposed estimator of the mode, based on densest half ranges, has a much lower bias while having similar robustness. Like the median, this mode estimator has the highest breakdown point possible: the estimator has meaning if less than half the sample consists of outliers. The mode is more robust than the median in that the mode estimates are unaffected by outliers, whereas the median is influenced by each outlier. Robustness in this sense is quantified by the rejection point, the largest absolute value that is not rejected, which is low for the mode but infinite for the median. Even though the median is changed less by contamination near the location than is the mode, outliers generally pose more of a problem to estimation than contamination near the location, so the mode is more robust for data that may have a large number of outliers. A robust estimator of skewness is based on this mode estimator.