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In data analysis, anomaly detection (also referred to as outlier detection and sometimes as novelty detection) is generally understood to be the identification of rare items, events or observations which deviate significantly from the majority of the data and do not conform to a well defined notion of normal behavior. [1]
In data sets containing real-numbered measurements, the suspected outliers are the measured values that appear to lie outside the cluster of most of the other data values. The outliers would greatly change the estimate of location if the arithmetic average were to be used as a summary statistic of location.
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.
The resulting values are quotient-values and hard to interpret. A value of 1 or even less indicates a clear inlier, but there is no clear rule for when a point is an outlier. In one data set, a value of 1.1 may already be an outlier, in another dataset and parameterization (with strong local fluctuations) a value of 2 could still be an inlier.
The idea behind Chauvenet's criterion finds a probability band that reasonably contains all n samples of a data set, centred on the mean of a normal distribution.By doing this, any data point from the n samples that lies outside this probability band can be considered an outlier, removed from the data set, and a new mean and standard deviation based on the remaining values and new sample size ...
Where gap is the absolute difference between the outlier in question and the closest number to it. If Q > Q table, where Q table is a reference value corresponding to the sample size and confidence level, then reject the questionable point. Note that only one point may be rejected from a data set using a Q test.
A typical strategy to account for, without eliminating altogether, these outlier values is to 'reset' outliers to a specified percentile (or an upper and lower percentile) of the data. For example, a 90% winsorization would see all data below the 5th percentile set to the 5th percentile, and all data above the 95th percentile set to the 95th ...
The sample maximum and minimum are the least robust statistics: they are maximally sensitive to outliers.. This can either be an advantage or a drawback: if extreme values are real (not measurement errors), and of real consequence, as in applications of extreme value theory such as building dikes or financial loss, then outliers (as reflected in sample extrema) are important.