DoubleBisquareWeightingFunction Class

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

Inheritance Hierarchy

SystemObject
CenterSpace.NMath.CoreDoubleLeastSqWeightingFunction
CenterSpace.NMath.CoreDoubleBisquareWeightingFunction

Namespace: CenterSpace.NMath.Core
Assembly: NMath (in NMath.dll) Version: 7.4

Syntax

[SerializableAttribute]
public class DoubleBisquareWeightingFunction : DoubleLeastSqWeightingFunction

<SerializableAttribute>
Public Class DoubleBisquareWeightingFunction
	Inherits DoubleLeastSqWeightingFunction

[SerializableAttribute]
public ref class DoubleBisquareWeightingFunction : public DoubleLeastSqWeightingFunction

[<SerializableAttribute>]
type DoubleBisquareWeightingFunction = 
    class
        inherit DoubleLeastSqWeightingFunction
    end

The DoubleBisquareWeightingFunction type exposes the following members.

Constructors

	Name	Description
	DoubleBisquareWeightingFunction	Constructs an instance of DoubleBisquareWeightingFunction with the default tuning factor.
	DoubleBisquareWeightingFunction(Double)	Constructs an instance of DoubleBisquareWeightingFunction with the given tuning factor.
	DoubleBisquareWeightingFunction(DoubleBisquareWeightingFunction)	Copy constructor. Creates an instance of DoubleBisquareWeightingFunction that is a deep copy of other.
	DoubleBisquareWeightingFunction(DoubleMatrix)	Constructs an instance of DoubleBisquareWeightingFunction for the given matrix with the default tuning factor.
	DoubleBisquareWeightingFunction(DoubleMatrix, Double)	Constructs a DoubleBisquareWeightingFunction for the specified matrx and tuning factor.

Properties

	Name	Description
	TuningConstant	Gets and sets the tuning constant. (Inherited from DoubleLeastSqWeightingFunction)

Methods

	Name	Description
	AdjustedResiduals	Returns a vector of adjusted residuals for the weighted least squares problem: Ax = b. (Inherited from DoubleLeastSqWeightingFunction)
	Clone	Creates a deep copy of this weighting. (Overrides DoubleLeastSqWeightingFunctionClone)
	GetWeights	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))
	Initialize	Performs initialization of the weighting function based on the matrix A in the weighted least squares problem: Ax - b. (Inherited from DoubleLeastSqWeightingFunction)
	MedianAbsDeviation	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)

Fields

	Name	Description
	adjFactor_	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)
	cols_	Number of columns in the matrix A in the least squares problem. Ax = b. (Inherited from DoubleLeastSqWeightingFunction)
	DEFAULT_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.
	rows_	Number of rows in the matrix A in the least squares problem. Ax = b. (Inherited from DoubleLeastSqWeightingFunction)
	tuningConstant_	Tuning constant used in the weighting function. Implementing classes should provide this value. (Inherited from DoubleLeastSqWeightingFunction)

Remarks

Applies the bisquare weighting formula to a set of adjusted residuals.