﻿DoubleBisquareWeightingFunction Class   # 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 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.
Top Properties
NameDescription TuningConstant
Gets and sets the tuning constant.
(Inherited from DoubleLeastSqWeightingFunction.)
Top Methods
NameDescription 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.)
Top Fields
NameDescription 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.)
Top Remarks
Applies the bisquare weighting formula to a set of adjusted residuals. See Also