robloss.gn: Generalized Robut loss function.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Resturn Generalized robust loss function for minimization purpose to find the Generalized M-estimate. Generalized M-estimate required correlation or covariance matrix of data, then the model transform and estimated.

Usage

robloss.gn(formula, data, start, robfunc, rmat, control = nlr.control(robscale = T), ...)

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.
rmat	R matrix, is cholesky decomposition of covariance matrix, the model transform by multiplying by R matrix.
control	list of nlr.control for controling convergence criterions.
...	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 \times r_i}{σ}\right)

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

The R matrix is rmat argument.

Value

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, transformed by R.
hessh.p1	hessian of loss function part1
hessh.p2	hessian of loss function part2, in clasic this part removed but in robust statistics values are significant and can not be omited, See Riazoshams et al 1014
dtilda	D(thilda) part of hessian
fmod	computed function (transformed by R) contains response and or its gradient and hessian predictor, transformed also by R.
Fault	Fault object of error, if no error Fault number = 0 will return back.

Note

This function use in optimization functions, specially from nlmest.NLM, for where the covariance matrix or R matrix given, may not be called explicitly by user.

Generalized M-estimate might reperesent the autocorrelated or heteroscedastic variance case.

This function call by nlr, for compatibility it is better to call from nlr rather than 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

Examples

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

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