S archive: Hampel's Redescending rho Function

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rho.hampel Hampel's Redescending rho Function

DESCRIPTION

Integral of Hampel's redescending psi function.

USAGE

rho.hampel(u, a = 1.5, b = 3.5, c = 8)

REQUIRED ARGUMENTS

u numeric vector of residuals.

OPTIONAL ARGUMENTS

`a`		numeric constant.
`b`		numeric constant.
`c`		numeric constant.

VALUE

rho numeric vector like u giving the values of rho.

DETAILS

The values of rho are analagous sum of squared residuals. rho is actually the integral of Hampel's redescending psi function. The default values for the parameters are as in Stromberg (1993)

REFERENCES

Hampel, Ronchetti, Rousseeuw and Stahel (1986). Robust Statistics. Wiley, New York, page 150.

Yohai, V. J. (1987). High breakdown point and high efficiency robust estimates for regression. Ann. Statist. 15, 642-656.

Stromberg, A. J. (1993). Computation of high breakdown nonlinear regression parameters. J. Amer. Statist. Assoc. 88, 237-244.

Smyth, G. K., and Hawkins, D. M. (1999). Robust frequency estimation using elemental sets. Submitted. (Abstract - Zipped PostScript)

SEE ALSO

mmnl, mscale, psi.hampel, mmfreq, robfreq, rreg and wt.hampel in the S-Plus documentation.

EXAMPLES

The function mmnl uses rho.hampel.

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