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However, multiple iterations change the probabilities of detection, and the test should not be used for sample sizes of six or fewer since it frequently tags most of the points as outliers. [3] Grubbs's test is defined for the following hypotheses: H 0: There are no outliers in the data set H a: There is exactly one outlier in the data set
Some work has also examined outliers for nominal (or categorical) data. In the context of a set of examples (or instances) in a data set, instance hardness measures the probability that an instance will be misclassified ( 1 − p ( y | x ) {\displaystyle 1-p(y|x)} where y is the assigned class label and x represent the input attribute value for ...
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 ...
In the presence of outliers that do not come from the same data-generating process as the rest of the data, least squares estimation is inefficient and can be biased. Because the least squares predictions are dragged towards the outliers, and because the variance of the estimates is artificially inflated, the result is that outliers can be masked.
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 ...
Peirce's criterion does not depend on observation data (only characteristics of the observation data), therefore making it a highly repeatable process that can be calculated independently of other processes. This feature makes Peirce's criterion for identifying outliers ideal in computer applications because it can be written as a call function.
Random sample consensus (RANSAC) is an iterative method to estimate parameters of a mathematical model from a set of observed data that contains outliers, when outliers are to be accorded no influence [clarify] on the values of the estimates. Therefore, it also can be interpreted as an outlier detection method. [1]
Previously when assessing a dataset before running a linear regression, the possibility of outliers would be assessed using histograms and scatterplots. Both methods of assessing data points were subjective and there was little way of knowing how much leverage each potential outlier had on the results data.