PDbdp
  
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PDc

PDc computes breakdown point and efficiency associated with tuning constant alpha for minimum power divergence estimator

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Syntax

Description

example

bdp =PDc(alpha) PDc with just one output argument.

example

[bdp, eff] =PDc(___) PDc with 2 output arguments.

Examples

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  • PDc with just one output argument.

    • [bdp]=PDc(1)
    disp('Break down point')
    disp(bdp)

  • PDc with 2 output arguments.

    • alpha=1;
    [bdp,eff]=PDc(alpha)
    disp('Break down point and efficiency')
    disp(['alpha=' num2str(alpha)])
    disp(['bdp=' num2str(bdp)])
    disp(['eff=' num2str(eff)])

    Related Examples

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  • Breakdown point and efficiency.

    • Analysis of breakdown point and asymptotic efficiency at the normal distribution as a function of alpha in regression. 

    c=0.01:0.01:1;
    [bdp,eff]=PDc(c);
    subplot(2,1,1)
    plot(c,bdp)
    xlabel('$\alpha$','Interpreter','Latex','FontSize',16)
    ylabel('Breakdown point','Interpreter','none')
    subplot(2,1,2)
    plot(c,eff)
    xlabel('$\alpha$','Interpreter','Latex','FontSize',16)
    ylabel('Asymptotic efficiency','Interpreter','none')

    Input Arguments

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    alpha — tuning constant alpha. Scalar or Vector.

    Scalar greater than 0 which controls the robustness/efficiency of the estimator

    Data Types: single| double

    Output Arguments

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    bdp —bdp. Scalar

    Breakdown point associated to the supplied value of c

    eff —eff. Scalar

    Efficiency associated to the supplied value of c Remark: if alpha is a vector bdp and eff will also be vectors with the same size of alpha. For example bdp(3) and eff(3) are associated to alpha(3) ....

    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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