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TBpsider

TBpsider computes derivative of psi function (second derivative of rho function) for Tukey's biweight

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Syntax

Description

example

psider =TBpsider(u, c) Plot the derivative of Tukey's biweght psi function.

Examples

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  • Plot the derivative of Tukey's biweght psi function.

    • x=-6:0.01:6;
    c=1.5476;
    psiTBder=TBpsider(x,c);
    plot(x,psiTBder)
    xlabel('x','Interpreter','Latex')
    ylabel('$\psi''(x)$','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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    psider —derivative of psi function. Vector

    n x 1 vector which contains the values of the derivative of the Tukey biweight psi function associated to the residuals or Mahalanobis distances for the n units of the sample.

    More About

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    Additional Details

    Function TBpsider transforms vector x as follows

    Remark: Tukey's biweight psi-function is almost linear around u = 0 in accordance with Winsor's principle that all distributions are normal in the middle.

    This means that \psi (u)/u is approximately constant over the linear region of \psi, so the points in that region tend to get equal weight.

    References

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

    See Also

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