HAbdp

HAbdp finds the constant c associated to the supplied breakdown point

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Syntax

Description

example

ctun =HAbdp(bdp, p) Find constant c for bdp=0.5.

example

ctun =HAbdp(bdp, p, abc) Find constant c for bdp=0.5 when abc=[1.5 3.5 8].

Examples

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  • Find constant c for bdp=0.5.

    • The constant c associated to a breakdown point of 50 per cent in regression is 0.198131771596856 

    c=HAbdp(0.5,1);
disp(c);
        0.1981

  • Find constant c for bdp=0.5 when abc=[1.5 3.5 8].

    • The constant c associated to a breakdown point of 50 per cent in regression is 

    c=HAbdp(0.5,1,[1.5 3.5 8]);
disp(c);
        0.2119

    Input Arguments

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    bdp — breakdown point. Scalar.

    Scalar defining breakdown point (i.e a number between 0 and 0.5)

    Data Types: single|double

    p — number of response variables. Scalar.

    e.g. in regression p=1

    Data Types: single|double|int32|int64

    Optional Arguments

    abc — parameters of Hampel estimator. Vector.

    Vector of length 3 which contains the parameters of Hampel estimator. If vector abc is not specified it is set equal to [2, 4, 8]

    Example: [1.5,3.5,8]

    Data Types: double

    Output Arguments

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    ctun —Requested tuning constant. Scalar

    Tuning constatnt of Hampel rho function associated to requested breakdown point

    More About

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    Additional Details

    Function HApsi transforms vector u as follows.

    \[ HApsi(u) = \left\{ \begin{array}{cc} u & |u| <= a \\ a \times sign(u) & a <= |u| < b \\ a \frac{c-|u|}{c-b} \times sign(u) & b <= |u| < c \\ 0 & |u| >= c \end{array} \right. \]

    where $a$= ctun *param(1).

    $b$= ctun *param(2).

    $c$= ctun *param(3).

    The default is $a$= 2*ctun.

    $b$= 4*ctun.

    $c$= 8*ctun.

    It is necessary to have 0 <= a <= b <= c

    References

    Hoaglin, D.C., Mosteller, F., Tukey, J.W. (1982), "Understanding Robust and Exploratory Data Analysis", Wiley, New York.

    See Also

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