(CME) Classic multi stage estimate for nonlinear regression with heteroscedastic error, when variance is function of unkown parameters. The variance function model parameter estimate using pseudo chi-square likelihood of computed sample variance. dfr.hetro is derivative free estimate CME.
dfr.hetro(formula, data, start = getInitial(formula, data),
control = nlr.control(tolerance = 1e-05, minlanda = 1/2^10,
maxiter = 25 * length(start)), varmodel, tau = NULL, ...)nl.form object of the nonlinear function model.
list of data include responce and predictor.
list of parameter values of nonlinear model function (\(\theta\).
list of nlr.control for controling convergence criterions.
nl.fomr object of variance function model for heteroscedastic variance.
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, or optimization functions.
generalized fitt object nl.fitt.gn. The hetro slot include parameter estimate and other information of fitt for heteroscedastic variance model.
nonlinear regression parameter estimate of \(\theta\).
of fited model.
nl.form object of called nonlinear regression model.
computed response.
computed (right side of formula) at estimated parameter with gradient and hessian attributes.
list of curvatures, see curvature function.
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.
fittmethod object of method used for fitt.
list of called data.
Object of class "callorNULL" source function called for fitt.
Fault object of error, if no error Fault number = 0 will return back.
covariance matrix, diagonal of variance model predicted values.
cholesky decomposition of vm.
transformed of response by rm, include gradinet and hessian attributes.
transformed of predictor by rm, include gradinet and hessian attributes.
nl.fitt 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.
In stage 1 the nonlinear model parameter estimates by Classic OLS, Stage 2 compute sample variance of data, Stage 3 estimate the parameter of variance function model by maximizing the chi-square pseudo-likelihood function. Stage 4 estimate the final value of function model parameter by generalized least square. For optimization the derivative free Nelder-Mead is used.
Riazoshams, H,. 2010. Outlier detection and robust estimation methods for nonlinear regression having autocorrelated and heteroscedastic errors. PhD thesis disertation, University Putra Malaysia.
Riazoshams H, Midi H, and Ghilagaber G, 2018,. Robust Nonlinear Regression, with Application using R, Joh Wiley and Sons.
# NOT RUN {
ntpstart22=list(p1=.12,p2=7,p3=1,p4=160)
ntpstarttau22=list(tau1=-1.24,tau2=2.56,tau3=.03042)
datalist=list(xr=ntp$dm.k,yr=ntp$cm.k)
datalist[[nlrobjvarmdls3[[2]]$independent]]<-ntp$dm.k
ntpfit<- dfr.robhetro(formula=nlrobj1[[16]],data=datalist,start=ntpstart22,
robfunc=nl.robfuncs[["hampel"]], tau=ntpstarttau22,
varmodel=nlrobjvarmdls3[[2]],robscale=TRUE,method="NM",control=nlr.control(tolerance=1e-4,
maxiter=150))
ntpfit$parameters
# }
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