PDpsider

PDpsider computes derivative of psi function (second derivative of rho function) for minimum power divergence estimator

Syntax

Description

example

psider =PDpsider(u, alpha) Plot the second derivative of minimum power divergence estimator.

Examples

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  • Plot the second derivative of minimum power divergence estimator.
  • x=-6:0.01:6;
    alpha=1;
    c=2;
    psiPDder=PDpsider(x,c);
    plot(x,psiPDder)
    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

    alpha — tuning parameter. Scalar.

    Scalar in the interval (0,1] which controls the robustness/efficiency of the estimator (beta in regression or mu in the location case ...). The greater is alpha the greater is the bdp and smaller is the efficiency.

    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 psi function of minimum power divergence estimator associated to the residuals or Mahalanobis distances for the n units of the sample.

    More About

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    Additional Details

    Function PDpsider transforms vector u as follows \[ PDpsider(u)= \alpha (1- \alpha u^2) \exp{-\alpha u^2/2} \]

    References

    Riani, M. Atkinson, A.C., Corbellini A. and Perrotta A. (2020), Robust Regression with Density Power Divergence: Theory, Comparisons and Data Analysis, submitted.

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