OPTeff

OPTeff finds the constant c which is associated to the requested efficiency

Syntax

Description

example

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

Examples

expand all

  • 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=OPTeff(0.95,1)

    Related Examples

    expand all

  • 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

    expand all

    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 p=1

    Data Types: single|double|int32|int64

    Output Arguments

    expand all

    ceff —Requested tuning constant. Scalar

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

    More About

    expand all

    Additional Details

    $\rho$ ($\psi$) function which is considered is standardized using intervals 0---(2/3)c , (2/3)c---c, >c.

    $\rho$ function is

    \[ TBrho(u)= \left\{ \begin{array}{lr} 1.3846 \left(\frac{u}{c}\right)^2 & |\frac{u}{c}| \leq \frac{2}{3} \\ 0.5514-2.6917 \left(\frac{u}{c}\right)^2 +10.7668\left(\frac{u}{c}\right)^4-11.6640\left(\frac{u}{c}\right)^6+4.0375\left(\frac{u}{c}\right)^8 & \qquad \frac{2}{3} \leq |\frac{u}{c}|\leq 1 \\ 1 & |\frac{u}{c}|>1 \\ \end{array} \right. \]

    |t/c|>1 Therefore, to obtain the value of c for the (rho) psi function defined in the interval 0---2c, 2c---3c, >3c it is necessary to divide the output of function OPTeff by 3.

    References

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

    See Also

    | |

    This page has been automatically generated by our routine publishFS