Median Squared Error Metric

A Median Squared Error Metric is an estimator evaluation metric that is based on the median of the estimator's squared errors.

• Context:
  • …
• Counter-Example(s):
  • a Root Mean Squared Error Measure.
  • Median Absolute Error Measure.
  • Mean Squared Error.
  • Median Absolute Deviation.
  • AUC Measure.
• See: k-Medians Clustering, Squared Error, Maximum Likelihood Estimate, Bias of an Estimator, Unbiased Estimator, Standard Deviation, Root-Median-Square Deviation.

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References

2011

• (Witten & Frank, 2011) ⇒ Ian H. Witten, Eibe Frank, and Mark A. Hall. (2011). “Data Mining: Practical machine learning tools and techniques, third edition." Morgan Kaufmann. ISBN:0123748569
  • QUOTE: Chapter 11 Explorer: … LeastMedSq is a robust linear regression method that minimizes the median (rather than the mean) of the squares of divergences from the regression line (see Section 7.5, page 333) (Rousseeuw and Leroy, 1987). It repeatedly applies standard linear regression to subsamples of the data and outputs the solution that has the smallest median-squared error. ...

1987

• (Rousseeuw and Leroy, 1987) ⇒ Annick M. Leroy, and Peter J. Rousseeuw. “Robust Regression and Outlier Detection." J. Wiley&Sons, New York (1987).

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