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.
robloss.gn(formula, data, start, robfunc, rmat, control = nlr.control(robscale = T), ...)nl.form object of nonlinear regression model.
list of data include responce and predictor.
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.
nl.form of rho function. It must include tuning constants k0 and k1.
R matrix, is cholesky decomposition of covariance matrix, the model transform by multiplying by R matrix.
list of nlr.control for controling convergence criterions.
any other arguments might be used in formula, robfunc or tuning constants in rho function.
list of output:
sum of rho function, include attribute "gradient" and "hessian"
computed rho function and attributes of "gradient" and "hessian"
residuals, transformed by R.
hessian of loss function part1
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
D(thilda) part of hessian
computed function (transformed by R) contains response and or its gradient and hessian predictor, transformed also by R.
Fault object of error, if no error Fault number = 0 will return back.
Compute Loss function, sum of robust rho function to compute the M-estimate.
$$\ell(\theta)=\sum \rho\left(\frac{R \times r_i}{\sigma}\right)$$
Standard deviation \(\sigma\) must be included in start argument list with the name sigma.
The R matrix is rmat argument.
Riazoshams H, Midi H, and Ghilagaber G, 2018,. Robust Nonlinear Regression, with Application using R, Joh Wiley and Sons.
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