loss.robchis: Hetroscedastic chi-square robust loss function.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Compute the robustified chi-square pseoudo log likelihood,based on varaince model function.

\ell (\boldsymbol{θ},τ )=∑\{ w_i \log (H({x_i};τ) + ρ ≤ft[√ {{z_i}/ H({x_i};{σ ^2},λ )} \right] \}

Usage

  loss.robchis(formula, data, start, theta, varmodel, robfunc, ...)

Arguments

formula	nl.form object of nonlinear function f(x;θ).
data	list of data include responce, predictor or possibly predictor of variance model function (t), if not represented then the predict of nonlinear model function will be replaced in predictor variable of nonlinear variance model function that is Var(\varepsilon)=σ^2 H(f(θ),τ)
start	list of parameter values of variance model function (τ in H(t,τ)), initial value or increament during optimization procedure.
theta	list of model function parameter (θ in f(x,θ)).
varmodel	nl.form object of heteroscedastic variance model function. varmodel must return variance function not standard deviation. Include gradient and hessian.
robfunc	nl.form of rho function. It must include tuning constants k0 and k1.
...	extra argument might pass to nonlinear regression, heteroscedastic functions, or tuning constant and other parameters to robust loss rho function.

Details

For estimating variance model parameter τ, robustified form of chi-square pseudo likelihood is used as robust estimate. Based on calculating the sample variances.

Value

list od los function values:

value	value of minus loglikelihood of chi-square, include attribute "gradient"" and "hessian". These values use in optimization functions.
angvec	angular vector for checking the convergence.
angmat	angular matrix for checking convergence in optimization procedure.
refvar	refvar, sample variance ∑(wi * z) \over ∑(wi)
fmod	computed function model f(x,θ), include response, predictor and their gradient and hessian depends on the defined form of nonlinear function model.
varcomp	computed variance function model H(t,τ), include response or predictor and their gradient and hessian depends on the defined form of nonlinear function model.
vcmdata	list of data used in variance model function, that is varmodel$independent and varmodel$dependent typically is zi.
sourcefnc	source function from which this function is called. May be used in feature computing such as outlier detection measures.
rho	computed robust loss rho function. Include hessian and gradients.
zi	computed sample variance, which follows the chi-square distribution.

Note

This is used for robust estimates, for classic see loss.chis This is implemented for internal use, might not be called directly by user.

Author(s)

Hossein Riazoshams, 08/01/2010. Email: [e-mail] URL http://www.riazoshams.com/nlr/

References

Riazoshams H 2010 Outlier detection and robust estimation methods for nonlinear regression having autocorrelated and heteroscedastic errors.

See Also

nl.form, loss.chis

Examples

## The function is currently defined as
"loss.robchis"

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