nlr (version 0.1-3)

nl.robhetro: Robust Multi Stage Estimate.

Description

(RME) for nonlinear regression with heteroscedastic variance, when the variance of error is general parameteric function of unkown parameters. Robust form of CME (See nl.hetro).

Usage

nl.robhetro(formula, data, start = getInitial(formula, data), 
control = nlr.control(tolerance = 1e-05, minlanda = 1/2^10, 
maxiter = 25 * length(start)), robfunc, varmodel, tau = NULL, ...)

Arguments

formula

nl.form object of the nonlinear function model.

data

list of data include responce and predictor.

start

list of parameter values of nonlinear model function (\(\theta\).

control

list of nlr.control for controling convergence criterions.

robfunc

nl.form object of robust function used for downgrading.

varmodel

nl.fomr object of variance function model for heteroscedastic variance.

tau

list of initial values for variance model function varmodel argument.

…

extra arguments to nonlinear regression model, heteroscedastic variance function, robust loss function or its tuning constants.

Value

nl.fitt.rgn for heterogeneous and autocorrelated error (nonlinear fitt robust generalized) will return.

parameters

nonlinear regression parameter estimate of \(\theta\).

correlation

of fited model.

form

nl.form object of called nonlinear regression model.

response

computed response.

predictor

computed (right side of formula) at estimated parameter with gradient and hessian attributes.

curvature

list of curvatures, see curvature function.

history

matrix of convergence history, collumns include: convergence index, parameters, minimized objective function, convergence criterion values, or other values. These values will be used in plot function in ploting history.

method

fittmethod object of method used for fitt.

data

list of called data.

sourcefnc

Object of class "callorNULL" source function called for fitt.

Fault

Fault object of error, if no error Fault number = 0 will return back.

htheta

robust loss value including gradient and hessain attributes.

rho

computed robust rho function, including gradient and hessain attributes.

ri

estimated residuals, including gradient and hessain attributes.

curvrob

curvature

robform

nl.form object of robust loss rho function.

vm

covariance matrix, diagonal of variance model predicted values.

rm

cholesky decomposition of vm.

gresponse

transformed of response by rm, include gradinet and hessian attributes.

gpredictor

transformed of predictor by rm, include gradinet and hessian attributes.

hetro

nl.fitt.rob object of fited variance odel:

• parametersestimate of variance parameter \(\tau\)

• formnl.form object of called varmodel.

• predictorvariance model computed at estimated parameter, \(H(x;\hat\tau)\)

• responsesample variance computed used as response variable.

• historymatrix of convergence history, collumns include: convergence index, parameters, minimized objective function, convergence criterion values, or other values.

• methodfittmethod object of method used for fitt.

• dataresponse (\(z_i\)) and predictor t variable values, used to computing the variance model.

• sourcefncObject of class "callorNULL" source function called for fitt.

• FaultFault object of error, if no error Fault number = 0 will return back.

• hthetarobust loss value including gradient and hessain attributes, for variance model. In fact is loglikelihood values.

• rhocomputed robust rho function, including gradient and hessain attributes.

others

$refvar reference variance. variance of zi's.

Details

In stage 1 the nonlinear model parameter estimates by robust MM-estimate, Stage 2 compute robust sample variance of data, Stage 3 estimate the parameter of variance function model by maximizing the robustified form of chi-square pseudo-likelihood function. Stage 4 estimate the final value of function model parameter by generalized robust MM-estimate.

References

Riazoshams, H,. 2010. Outlier detection and robust estimation methods for nonlinear regression having autocorrelated and heteroscedastic errors. PhD thesis disertation, University Putra Malaysia.

See Also

fittmethod, nl.form, nl.fitt.rob, nl.fitt.rgn

Examples

# NOT RUN {
# ntp data fitt
# tolerance is set as 1e-3 for testing purposes
# is not accurate enough, user can increase it.
ntpstart=list(p1=.12,p2=6,p3=1,p4=33)
ntpstarttau=list(tau1=-.66,tau2=2,tau3=.04)
datalist=list(xr=ntp$dm.k,yr=ntp$cm.k)
datalist[[nlrobjvarmdls3[[2]]$independent]]<-ntp$dm.k
aa1 <- nl.robhetro(formula=nlrobj1[[16]],data=datalist,
start=ntpstart,robfunc=nl.robfuncs[["hampel"]],
tau=ntpstarttau,varmodel=nlrobjvarmdls3[[2]],robscale=T,method="NM",
control=nlr.control(tolerance=1e-4))
aa1$parameters
# }