TBc

TBc computes breakdown point and efficiency associated with constant c for Tukey's biweight

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Syntax

Description

example

bdp =TBc(c, v) Tbc with just one output argument.

example

bdp =TBc(c, v, shapeeff) Tbc with 2 output arguments.

example

[bdp, eff] =TBc(___) Find also approximate value of scale efficiency (for R comparability).

example

[bdp, eff, approxsheff] =TBc(___) Breakdown point and efficiency.

Examples

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  • Tbc with just one output argument.

    • [bdp]=TBc(2,1)
disp('Break down point')
disp(bdp)

  • Tbc with 2 output arguments.

    • [bdp,eff]=TBc(2,1)
disp('Break down point and efficiency')
disp(bdp)
disp(eff)

  • Breakdown point and efficiency.

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

    c=1:0.01:6;
[bdp,eff]=TBc(c,1);
subplot(2,1,1)
plot(c,bdp)
xlabel('c','Interpreter','Latex','FontSize',16)
ylabel('Breakdown point','Interpreter','none')
subplot(2,1,2)
plot(c,eff)
xlabel('c','Interpreter','Latex','FontSize',16)
ylabel('Asymptotic efficiency','Interpreter','none')

    Input Arguments

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    c — tuning constant c. Scalar.

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

    Data Types: single| double

    v — number of response variables. Scalar.

    Number of variables of the dataset (for regression v=1)

    Data Types: single| double

    Optional Arguments

    shapeeff — location or shape efficiency. Scalar.

    If shapeeff=1, the efficiency is referred to the shape else (default) is referred to the location estimator

    Example: 1

    Data Types: 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 c is a vector bdp and eff will also be vectors with the same size of c. For example bdp(3) and eff(3) are associated to c(3) ....

    approxsheff —Approximate value of efficiency. Scalar

    Approximate value of efficiency in case input option shapeeff=1 and v>1.

    This output is left for comparability with the value which comes out from R library robustbase.

    References

    Hampel, F.R., Rousseeuw, P.J. and Ronchetti, E. (1981), The Change-of-Variance Curve and Optimal Redescending M-Estimators, "Journal of the American Statistical Association", Vol. 76, pp. 643-648. [HRR]

    See Also

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