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DESCRIPTION

Estimates a nonlinear regression equation using 95% efficient MM estimation. User supplies the regression function and its gradient matrix.

 

USAGE

mmnl(X,y,b,fun,grad,scale=NULL,trace=F)

 

REQUIRED ARGUMENTS

X		numeric design matrix. Number of rows must agree with y.
y		numeric vector of observations.
b		numeric vector of starting values for the parameters.
fun		function giving vector of fitted values as a function of X and b.
grad		function giving gradient matrix as a function of X and b.

 

OPTIONAL ARGUMENTS

scale		numeric constant giving scale of the residuals. By default this is mscale(y - fun(X,b)).
trace		logical constant. If true, parameters and criterion are printed at each iteration.

 

VALUE

b		numeric vector of estimated parametes.
fitted		numeric vector of same length as y of fitted values.
residuals		numeric vector of same length as y of residuals.
scale		numeric constant giving the estimated or input scale.
criterion		numeric constant giving the estimated criterion functoin.

 

DETAILS

Uses Hampel's redescending psi function. The estimators simultaneously have high breakdown and 95% efficiency under normal errors given consistent high breakdown starting values.

 

REFERENCES

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. (2000). Robust frequency estimation using elemental sets. Journal of Computational and Graphical Statistics 9, 196-214. (Abstract - Zipped PostScript)

 

SEE ALSO

mscale, rho.hampel, psi.hampel, mmfreq, robfreq

 

EXAMPLES

The function mmfreq gives an example of using mmnl.

Gordon Smyth. Copyright © 1996-2016. Last modified: 10 February 2004