dfr.robloss: Robut loss function.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Resturn robust loss function for minimization purpose to find the M-estimate. It is used in dfrmest.NLM function for derivative free purpose. Gradient and hessian are computed numerically.

Usage

dfr.robloss(formula, data, start, robfunc, control = nlr.control(), rmat = NULL, ...)

Arguments

formula	nl.form object of nonlinear regression model.
data	list of data include responce and predictor.
start	list of parameter values of nonlinear model function (θ in f(x,θ)), initial values or increament during optimization procedure. It must include scale sigma (standard deviation), if not included Fault(9) will be returned.
robfunc	nl.form of rho function. It must include tuning constants k0 and k1.
control	list of nlr.control for controling convergence criterions.
rmat	R-Matrix for transforming, it might be cholesky decomposition of covariance matrix.
...	any other arguments might be used in formula, robfunc or tuning constants in rho function.

Details

Compute Loss function, sum of robust rho function to compute the M-estimate.

\ell(θ)=∑ ρ≤ft(\frac{r_i}{σ}\right)

Standard deviation σ must be included in start argument list with the name sigma.

gradient and hessian attributes compute numerically.

Value

result <- list(htheta=htheta,rho=robvalue,ri=rsd,fmod=fmod,Fault=Fault2) list of output:

htheta:	sum of rho function, include attribute "gradient" and "hessian"
rho:	computed rho function and attributes of "gradient" and "hessian"
ri:	residuals
fmod:	computed function contains esponse and or its gradient and hessian predictor and or its gradient & hessian
Fault:	Fault object of error, if no error Fault number = 0 will return back.

Note

All functions should have gradient and hessian in attributes. For derivative free purpose the dfr.robloss can be used. It is designed for internal use, might not call directly by user.

Author(s)

Hossein Riazoshams, May 2014. Email: [e-mail] URL http://www.riazoshams.com/nlr/

References

Riazoshams H, Midi H, and Ghilagaber G, 2018,. Robust Nonlinear Regression, with Application using R, Joh Wiley and Sons.

See Also

nl.form, nlr.control, nlmest.NLM, dfr.robloss, robloss

Examples

## The function is currently defined as
"dfr.robloss"

nlr documentation built on July 31, 2019, 5:09 p.m.