HUwei

HUwei computes weight function psi(u)/u for Huber

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Syntax

Description

example

wei =HUwei(u, c) Plot Huber weights.

Examples

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  • Plot Huber weights.

    • x=-6:0.01:6;
weiHU=HUwei(x,2);
plot(x,weiHU)
xlabel('x','Interpreter','Latex')
ylabel('$W (x) =\psi(x)/x$','Interpreter','Latex')

    Input Arguments

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    u — scaled residuals or Mahalanobis distances. Vector.

    n x 1 vector containing residuals or Mahalanobis distances for the n units of the sample

    Data Types: single| double

    c — tuning parameters. Scalar.

    Scalar greater than 0 which controls the robustness/efficiency of the estimator (beta in regression or mu in the location case ...)

    Data Types: single| double

    Output Arguments

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    wei —Weights vector. Vector

    n x 1 vector containing the Huber weights associated to the scaled residuals or Mahalanobis distances for the n units of the sample.

    More About

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    Additional Details

    Function HUwei transforms vector u as follows \[ HUwei(u)= \left\{ \begin{array}{cc} 1 & |u/c| \leq 1 \\ c \times \frac{\mbox{sign}(u)}{u} & |u/c|>1 \\ \end{array} \right. \] See equation (2.32) p. 28 of Maronna et al. (2006)

    References

    Maronna, R.A., Martin D. and Yohai V.J. (2006), "Robust Statistics, Theory and Methods", Wiley, New York.

    Riani, M., Cerioli, A. and Torti, F. (2014), On consistency factors and efficiency of robust S-estimators, "TEST", Vol. 23, pp. 356-387.

    http://dx.doi.org/10.1007/s11749-014-0357-7

    See Also

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