nlr (version 0.1-3)

dfr.robloss: Robut loss function.

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 (\(\theta\) in \(f(x,\theta)\)), 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.

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.

Details

Compute Loss function, sum of robust rho function to compute the M-estimate. $$\ell(\theta)=\sum \rho\left(\frac{r_i}{\sigma}\right)$$ Standard deviation \(\sigma\) must be included in start argument list with the name sigma.

gradient and hessian attributes compute numerically.

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

# NOT RUN {
## The function is currently defined as
"dfr.robloss"
# }