================= 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.