================= Hampel Identifier ================= :doc:/WorkProcessClassifiers/GlobalAlgorithm/index - :doc:/WorkProcessClassifiers/OneDimensionalAlgorithm/index *Hampel Identifier* algorithm decides whether a value is a value outside the region of interest based on that value's distance from the estimated median distribution. Generally, if .. math:: |Y_i - \text{Median}(Y)| > 3 \cdot \text{MAD} \, \text{,} the data point is considered outside the region of interest. :math:\text{Median}(Y) is the *Median*, :math:Y_i is :math:i\ th element of :math:Y and :math:\text{MAD} corresponds to the *Median Absolute Deviation* value. .. rubric:: Input Parameters +--------------------+--------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +====================+============================================+========================================+==================================================+=========+ | :math:Y | :math:Y \in \mathbb R^N | :math:N \in \mathbb{N} | Input data sequence of length :math:N | | +--------------------+--------------------------------------------+----------------------------------------+--------------------------------------------------+---------+ .. rubric:: Output Parameters +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ | Parameter | Type | Constraint | Description | Remarks | +============================+====================================================+============+===========================================================================================+=========+ | :math:\hat{Y} | :math:\hat{Y} \in \mathbb R^N | | Values in the :math:Y list which are outside the region of interest are marked | | +----------------------------+----------------------------------------------------+------------+-------------------------------------------------------------------------------------------+---------+ .. rubric:: Tool Support * :doc:/Tools/RTool/index .. rubric:: Single Steps using the Algorithm * :doc:/DataPreprocessing/DataCleaning/OutlierDetection/OutlierDetectionWithHampelIdentifier/index .. rubric:: References - R.K.\ Pearson, Mining Imperfect Data, Society for Industrial and Applied Mathematics, Philadelphia, PA., 2005.