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The statistician and historian of statistics Stephen M. Stigler wrote the following about Benjamin Peirce: [1] "In 1852 he published the first significance test designed to tell an investigator whether an outlier should be rejected (Peirce 1852, 1878).
The book has seven chapters. [1] [4] The first is introductory; it describes simple linear regression (in which there is only one independent variable), discusses the possibility of outliers that corrupt either the dependent or the independent variable, provides examples in which outliers produce misleading results, defines the breakdown point, and briefly introduces several methods for robust ...
The M in M-estimation stands for "maximum likelihood type". The method is robust to outliers in the response variable, but turned out not to be resistant to outliers in the explanatory variables (leverage points). In fact, when there are outliers in the explanatory variables, the method has no advantage over least squares.
Also referred to as frequency-based or counting-based, the simplest non-parametric anomaly detection method is to build a histogram with the training data or a set of known normal instances, and if a test point does not fall in any of the histogram bins mark it as anomalous, or assign an anomaly score to test data based on the height of the bin ...
The modified Thompson Tau test is used to find one outlier at a time (largest value of δ is removed if it is an outlier). Meaning, if a data point is found to be an outlier, it is removed from the data set and the test is applied again with a new average and rejection region. This process is continued until no outliers remain in a data set.
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In statistics, Grubbs's test or the Grubbs test (named after Frank E. Grubbs, who published the test in 1950 [1]), also known as the maximum normalized residual test or extreme studentized deviate test, is a test used to detect outliers in a univariate data set assumed to come from a normally distributed population.
[1] The book debuted at number one on the bestseller lists of The New York Times and The Globe and Mail, holding the position on the former for eleven consecutive weeks. Generally well received by critics, Outliers was considered more personal than Gladwell's other works, and some reviews commented on how much Outliers felt like an ...