initial: Initial coefficients and covariance estimators for PFC model
In meszre/tauPFC: Computes Robust Estimators for the PFC Model

Description Usage Arguments Details Value See Also Examples

Compute initial estimators for the coefficient matrix and the covariance matrix. Both are strongly robust to the presence of outliers in the sample but possibly inefficient. They are a good starting point for tau-estimators for PFC model.

1	initial(X, Fy, aux, efficiency = 0.85)

`X`	vector of response variables in the inverse model, n x p matrix, each row is a response vector
`Fy`	vector of covariates in the inverse problem, vector containing functions of the response variable in the original multiple regression problem. Is a n x p matrix, each row is the corresponding response vector
`aux`	list containing the constants for the tau-scale (with components c1, k1, c2, k2, as described in `kappa_and_c`)
`efficiency`	required efficiency for initial robust estimator

This function computes the coefficient matrix concatenating the coefficients resulting from the fitting of univariate regressions using a robust estimator with high breakdown point and high efficiency (require "robustbase"). Univariate estimators are computed using lmrob "lmRob" function. It computes a robust estimator of errors covariance matrix (require "rrcov").

The estimation is given as a list with components

`beta0`	coefficient matrix
`delta0`	S covariance matrix of residuals

For the final estimation use tauestimate with this initial estimator as an input

p=10
mutrue=rep(0,p)
gamatrue=as.matrix(c(1,rep(0,p-1)))
betatrue=t(as.matrix(c(1,1)))

data_sim=generate(p,n=200,mutrue,gamatrue,betatrue,sigmatrue=1)

aux=kappa_and_c(p,efficiency=0.85)
initial(data_sim$X,data_sim$Fy,aux,efficiency=0.85)