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HAc
  
HApsi
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HAeff

HAeff finds the tuning constant that guarrantees a requested asymptotic efficiency

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Syntax

Description

example

ceff =HAeff(eff, v) Find c for fixed efficiency.

example

ceff =HAeff(eff, v, abc) Example where three input parameters are supplied.

Examples

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  • Find c for fixed efficiency.

    • The constant c associated to a nominal location efficiency of 95% in regression is c = 0.690998716841394 

    c=HAeff(0.95,1)

  • Example where three input parameters are supplied.

    • Find constant c associated to a nominal location efficiency of 95 per cent in regression when tun=[1.5,3.5,8]. 

    tun=[1.5,3,8];
    c=HAeff(0.95,1,tun);

    Input Arguments

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    eff — efficiency. Scalar.

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

    Generally eff=0.85, 0.9 or 0.95.

    Data Types: single| double

    v — number of response variables. Scalar.

    Number of variables of the dataset (for regression v=1) UP TO NOW v=1 (JUST REGRESSION) TO DO FOR MULTIVARIATE ANALYSIS

    Data Types: single| double

    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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    ceff —Requested tuning constant. Scalar

    Tuning constatnt of Hampel rho function associated to requested value of efficiency

    More About

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    Additional Details

    Function HApsi transforms vector u as follows.

    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.

    Parameter ctun multiplies parameters (a,b,c) of Hampel estimator.

    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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