PDpsix

PDpsix computes psi function (derivative of rho function) times x for minimum density power divergence estimator

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Syntax

Description

example

psix =PDpsix(u, alpha) Plot of psi function (derivative of rho function) times x for minimum density power divergence estimator.

Examples

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  • Plot of psi function (derivative of rho function) times x for minimum density power divergence estimator.

    • x=-6:0.01:6;
psixPD=PDpsix(x,1);
plot(x,psixPD)
xlabel('x','Interpreter','Latex')
ylabel('$\psi_\alpha (x)$','Interpreter','Latex')

    Input Arguments

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    u — scaled residuals or Mahalanobis distances. Vector.

    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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    psix —Values of PD psi(u)*u function associated to the residuals or Mahalanobis distances for the n units of the sample. vector

    More About

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    Additional Details

    Function PDpsix transforms vector u as follows \[ PDpsix(u,alpha)= \alpha u^2 \exp(-\alpha (u^2/2)); \]

    References

    Riani, M. Atkinson, A.C., Corbellini A. and Perrotta A. (2020), Robust Regression with Density Power Divergence: Theory, Comparisons and Data Analysis, Entropy, Vol. 22, 399.

    https://www.mdpi.com/1099-4300/22/4/399

    See Also

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