loss.chis: Hetroscedastic chi-square loss function.

In nlr: Nonlinear Regression Modelling using Robust Methods

Description

Compute the minus of chi-square pseoudo log likelihood,based on varaince model function. \ell ({σ ^2},λ ) = ∑ \{ w_i \log (\tilde H({x_i};{σ ^2},λ )) + {z_i}/\tilde H({x_i};{σ ^2},λ ) \}

Usage

  loss.chis(formula, data, start, theta, varmodel, ...)

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.
...	extra argument might pass to nonlinear regression or heteroscedastic functions.

Details

For estimating variance model parameter τ, chi-square pseudo chi square is used as classic 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.
zi	computed sample variance, which follows the chi-square distribution.

Note

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

Author(s)

Bunke, O., Droge, B., Polzehl

References

Bunke, O., Droge, B., Polzehl, J. Splus tools for model selection in nonlinear regression (1998) Computational Statistics, 13 (2), pp. 257-281.

See Also

loss.robchis, nlr

Examples

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

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