TBeff

Tbeff finds the constant c which is associated to the requested efficiency for Tukey's biweight

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Syntax

  • ceff=TBeff(eff, v)example
  • ceff=TBeff(eff, v, shapeeff)example
  • ceff=TBeff(eff, v, shapeeff, approxsheff)example

Description

example

ceff =TBeff(eff, v) Find c for a given efficiency.

example

ceff =TBeff(eff, v, shapeeff)

example

ceff =TBeff(eff, v, shapeeff, approxsheff) Find shape efficiency.

Examples

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  • Find c for a given efficiency.

    • The constant c associated to a nominal location efficiency of 95% in regression is c = 4.685064948559557 

    c=TBeff(0.95,1)

  • c=TBeff(0.95,1,1)

  • Find shape efficiency.

    • Compare constant c for the range of values of p from 1 to 200 using approximate and exact formula for fixed shape efficiency Number of variables 

    p=200;
    pp=1:1:p;
    % Initialize the matrix which stores the values of c for the two
    % methods
    cc=[pp' zeros(p,2)];
    eff=0.75;
    % eff=0.99;
    for i=pp
    % Use exact formula for finding the value of c associated to a fixed
    % level of shape efficiency
    cc(i,2)=TBeff(eff,i,1);
    % Use approximate formula for finding the value of c associated to a fixed
    % level of shape efficiency
    cc(i,3)=TBeff(eff,i,1,1);
    end
    figure
    plot(cc(:,1),cc(:,2),'LineStyle','-','LineWidth',2)
    hold('on')
    plot(cc(:,1),cc(:,3),'LineStyle','-.','LineWidth',2)
    legend('True value of c', 'Approximate value of c','Location','best')
    xlabel('Number of variables')
    ylabel('Value of c')

    Input Arguments

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    eff — required efficiency. 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 p=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

    Example: 'shapeeff',1

    Data Types: double

    approxsheff — approximate or exact calculations. Dummy scalar.

    If 1, when p > 1 the approximate formula for scale efficiency is used else (default) the exact formula of the variance of the robust estimator of the scale is used

    Example: 'approxsheff',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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