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DoubleBisquareWeightingFunction Class

Class DoubleBisquareWeightingFunction implements the bisquare weighting function for Iteratively Reweighted Least Squares (IRLS).
Inheritance Hierarchy

Namespace:  CenterSpace.NMath.Core
Assembly:  NMath (in NMath.dll) Version: 7.3
Syntax
[SerializableAttribute]
public class DoubleBisquareWeightingFunction : DoubleLeastSqWeightingFunction

The DoubleBisquareWeightingFunction type exposes the following members.

Constructors
  NameDescription
Public methodDoubleBisquareWeightingFunction
Constructs an instance of DoubleBisquareWeightingFunction with the default tuning factor.
Public methodDoubleBisquareWeightingFunction(Double)
Constructs an instance of DoubleBisquareWeightingFunction with the given tuning factor.
Protected methodDoubleBisquareWeightingFunction(DoubleBisquareWeightingFunction)
Copy constructor. Creates an instance of DoubleBisquareWeightingFunction that is a deep copy of other.
Public methodDoubleBisquareWeightingFunction(DoubleMatrix)
Constructs an instance of DoubleBisquareWeightingFunction for the given matrix with the default tuning factor.
Public methodDoubleBisquareWeightingFunction(DoubleMatrix, Double)
Constructs a DoubleBisquareWeightingFunction for the specified matrx and tuning factor.
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Properties
  NameDescription
Public propertyTuningConstant
Gets and sets the tuning constant.
(Inherited from DoubleLeastSqWeightingFunction.)
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Methods
  NameDescription
Public methodAdjustedResiduals
Returns a vector of adjusted residuals for the weighted least squares problem: Ax = b.
(Inherited from DoubleLeastSqWeightingFunction.)
Public methodClone
Creates a deep copy of this weighting.
(Overrides DoubleLeastSqWeightingFunctionClone.)
Public methodGetWeights
Computes the bisquare weights for the residuals using the formula: w(r) = (1 - r^2)^2 if |r| is less than 1 and w(r) = 0 if |r| is greater or equal to 1. Here r is the adjusted redisuals from the AdjustedResidual function of the base class DoubleLeastSqWeightingFunction.
(Overrides DoubleLeastSqWeightingFunctionGetWeights(DoubleVector, DoubleVector).)
Public methodInitialize
Performs initialization of the weighting function based on the matrix A in the weighted least squares problem: Ax - b.
(Inherited from DoubleLeastSqWeightingFunction.)
Public methodMedianAbsDeviation
Returns the Mean Absolute Deviation of a vector of values. The mean absolute deviation is an estimate of the standard deviation of the vector of residuals normalized to make the estimate unbiased for the normal distribution.
(Inherited from DoubleLeastSqWeightingFunction.)
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Fields
  NameDescription
Protected fieldadjFactor_
Adjustment factor used in computing the adjusted residuals. It is given by the formula: 1.0 / sqrt(1 - h). Where, h is the vector of leverage values. The leverage values are the main diagonal of the hat matrix H = A((A'A)^-1)A'.
(Inherited from DoubleLeastSqWeightingFunction.)
Protected fieldcols_
Number of columns in the matrix A in the least squares problem. Ax = b.
(Inherited from DoubleLeastSqWeightingFunction.)
Public fieldStatic memberDEFAULT_TUNING_FACTOR
Default value for the bisquare weighting tuning factor. If the response is normally distributed, the default tuning factor gives coefficient estimates that are approximately 95% as statistically efficient as the ordinary least squares estimates.
Protected fieldrows_
Number of rows in the matrix A in the least squares problem. Ax = b.
(Inherited from DoubleLeastSqWeightingFunction.)
Protected fieldtuningConstant_
Tuning constant used in the weighting function. Implementing classes should provide this value.
(Inherited from DoubleLeastSqWeightingFunction.)
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Remarks
Applies the bisquare weighting formula to a set of adjusted residuals.
See Also