BiweightLocation

BiweightLocation[list]

gives the value of the biweight location estimator of the elements in list.

BiweightLocation[list,c]

gives the value of the biweight location estimator with scaling parameter c.

Details and Options

  • BiweightLocation is a robust location estimator.
  • BiweightLocation is given by a weighted mean of the elements. Elements farther from the center have lower weights.
  • The width scale of the weight function is controlled by a parameter c. Larger c indicates more data values are included in the computation of the statistic, and vice versa. »
  • For the list {x1,x2,,xn}, the value of the biweight location estimator is given by , where and is Median[{x1-x*,x2-x*,,xn-x*}]. The value x* of the estimator is computed iteratively, with the initial value chosen automatically by default.
  • BiweightLocation[list] is equivalent to BiweightLocation[list,6].
  • BiweightLocation[{{x1,y1,},{x2,y2,},}] gives {BiweightLocation[{x1,x2,}],BiweightLocation[{y1,y2,}],}.
  • BiweightLocation allows c to be any positive real number.
  • The following options can be given:
  • AccuracyGoalAutomaticthe accuracy sought
    MaxIterationsAutomaticmaximum number of iterations to use
    MethodAutomaticmethod to use
    PrecisionGoalAutomaticthe precision sought
    WorkingPrecisionMachinePrecisionthe precision used in internal computations
  • The setting Method{"InitialPoint"x0} allows for a custom initial value .

Examples

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Basic Examples  (3)

BiweightLocation of a list:

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BiweightLocation of columns of a matrix:

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BiweightLocation of a list with scaling parameter 7:

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Scope  (6)

Options  (2)

Applications  (3)

Properties & Relations  (3)

Neat Examples  (2)

See Also

Median  Mean  TrimmedMean  WinsorizedMean  SpatialMedian  CentralFeature  BiweightMidvariance

Introduced in 2017
(11.1)