NMath Reference Guide

## Double |

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

Inheritance Hierarchy

SystemObject

CenterSpace.NMath.CoreDoubleLeastSqWeightingFunction

CenterSpace.NMath.CoreDoubleBisquareWeightingFunction

CenterSpace.NMath.CoreDoubleLeastSqWeightingFunction

CenterSpace.NMath.CoreDoubleBisquareWeightingFunction

Syntax

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.

See Also