OPTbdp

OPTbdp finds the constant c associated to the supplied breakdown point

Description

c =OPTbdp(bdp, v) Find c given bdp.

Examples

expand all

Find c given bdp.

The constant c associated to a breakdown point of 50% in regression is c= 1.213897063441983

c=OPTbdp(0.5,1)

Input Arguments

bdp — breakdown point. Scalar.

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

Data Types: single|double

v — number of response variables. Scalar.

e.g. in regression p=1

Data Types: single|double|int32|int64

Output Arguments

c —Requested tuning constant. Scalar

Tuning constatnt of optimal rho function associated to requested breakdown point

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

$\rho$ function is

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

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 OPTbdp by 3.

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