HUpsider

HUpsider computes derivative of psi function (second derivative of rho function) for Huber

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Syntax

Description

example

psider =HUpsider(u, c) Plot of derivative of psi function.

Examples

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  • Plot of derivative of psi function.

    • x=-6:0.01:6;
psiHUder=HUpsider(x,2);
plot(x,psiHUder)
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 for the n units of the sample scaled residuals or Mahalanobis distances

    Data Types: single| double

    c — tuning constant. 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 Huber 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 HUpsider transforms vector x as follows HUpsider(x)= \[ HUpsider(u)= \left\{ \begin{array}{cc} 1 & \mbox{if } |u/c| \leq 1 \\ 0 & |u/c|>1 \\ \end{array} \right. \]

    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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