HUeff

HUeff finds the constant c which is associated to the requested efficiency for Tukey biweight estimator

Syntax

Description

example

ceff =HUeff(eff, v) Find c in regression for 95 per cent efficiency.

example

ceff =HUeff(eff, v, shapeeff) Analyze constant c as a function of eff.

Examples

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  • Find c in regression for 95 per cent efficiency.
  • The constant c associated to a nominal location efficiency of 95% in regression is c = 1.344997508513144

    c=HUeff(0.95,1)

  • Analyze constant c as a function of eff.
  • Initialize the matrix which stores the values of c for the two methods

    eff=[0.70:0.0001:0.9999];
    cc=[eff' zeros(length(eff),1)];
    for i=1:length(eff)
    % Use exact formula for finding the value of c associated to a fixed
    % level of shape efficiency
    cc(i,2)=TBeff(eff(i),1);
    end
    figure
    plot(cc(:,1),cc(:,2),'LineStyle','-','LineWidth',2)
    xlabel('Effciency')
    ylabel('Value of c')

    Input Arguments

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    eff — required efficienty. Scalar.

    Scalar which contains the required efficiency (of location or scale estimator).

    Data Types: single|double Generally eff=0.85, 0.9 or 0.95

    v — Number of response variables. Scalar.

    e.g. in regression v=1 Now it is implemented just for v=1

    Data Types: single|double|int32|int64

    Optional Arguments

    shapeeff — Location or shape efficiency. Scalar.

    If 1, the efficiency is referred to shape else (default) is referred to location (not implemented yet)

    Example: 'shapeeff',1

    Data Types: double

    Output Arguments

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    ceff —Requested tuning constant. Scalar

    Tuning constatnt of Tukey Biweigh rho function associated to requested value of efficiency

    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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