Returns a vector of adjusted residuals for the weighted least squares problem: Ax = b.

Namespace:  CenterSpace.NMath.Matrix
Assembly:  NMath (in NMath.dll) Version: 5.1.0.0

Syntax

C#
public DoubleVector AdjustedResiduals(
	DoubleVector residuals
)
Visual Basic (Declaration)
Public Function AdjustedResiduals ( _
	residuals As DoubleVector _
) As DoubleVector
Visual C++
public:
DoubleVector^ AdjustedResiduals(
	DoubleVector^ residuals
)

Parameters

residuals
Type: CenterSpace.NMath.Core..::.DoubleVector
Actual residuals.

Return Value

Adjusted residuals.

Remarks

Adjusted residuals are computed according to the following formula: adjustedResiduals = residuals / (tuningConstant*s*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'. s is an estimate of the standard deviation of the error term given by: s = MAD / 0.6745 where MAD is the median absolute deviation of the residuals from their median. The constant 0.6745 makes the estimate unbiased for the normal distribution. tuningConstant is a tuning constant by which the residuals are divided before computing weights. Decreasing the tuning constant increases the downweight assigned to large residuals and increasing the tuning constant decreases the downweight assigned to large residuals.

See Also