RKeff

ROeff finds the constants c and M which are associated to the requested efficiency and ARP

Syntax

Description

example

c =RKeff(eff, v) Find c given a value of efficiency.

example

c =RKeff(eff, v, ARP) Find the value of c for efficiency which goes to 1.

example

[c, M] =RKeff(___)

Examples

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  • Find c given a value of efficiency.
  • The constant c associated to a nominal location efficiency of 95% in regression is c = 3.180662196584308

        [c,M]=RKeff(0.95,5,0.05)
    

  • Find the value of c for efficiency which goes to 1.
  •     ef=0.75:0.01:0.99;
        CC=[ef' zeros(length(ef),1)];
        jk=0;
        for j=ef
            jk=jk+1;
            CC(jk,2)=OPTeff(j,1)
        end
    
    

    Input Arguments

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    eff — required efficienty. 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.

    e.g. in regression v=1

    Data Types: single|double|int32|int64

    Optional Arguments

    ARP — asymptotic rejection probability. Scalar.

    The asymptotic rejection probability of an estimator is defined as the probability in large sample under a reference distribution that a Malanobis distance excees $c_0$, where $c_0=inf \{ u_0 | w(u)=0, \forall u>u_0 \}$.

    $w(u)$ is the weight function (defined in RKwei.m). In other words, given $c_0=sup(\rho(u))$,if an estimator is normed to the normal distribution ARP is $1-F_{\chi^2_v}(c_0^2)$.

    The default value of ARP is 0.05.

    Example: 0.04

    Data Types: double

    Output Arguments

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    c —Requested tuning constant. Scalar

    Tuning constatnt of Rocke rho function (translated Tukey Biweight) associated to requested efficiency and asymptotic rejection probability

    M —Requested tuning constant. Scalar

    Tuning constant of Rocke rho function (translated Tukey Biweight) associated to requested efficiency and asymptotic rejection probability

    References

    Maronna, R.A., Martin D. and Yohai V.J. (2006), "Robust Statistics, Theory and Methods", Wiley, New York.

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