# OPTeff

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

## Syntax

• ceff=OPTeff(eff,v)example

## Description

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

## 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=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

### 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

### ceff —Requested tuning constant. Scalar

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

$\rho$ ($\psi$) 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.

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