initial.RdCompute 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.
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
|
| 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 "robust"). 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
coefficient matrix
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)#> $beta0 #> [,1] [,2] [,3] #> [1,] -0.07545820 1.236930387 0.932612434 #> [2,] 0.09159632 -0.002129832 -0.014510932 #> [3,] 0.02939874 -0.076097885 0.028233235 #> [4,] 0.48227567 -0.607202284 0.136083197 #> [5,] 0.01435626 0.020433950 -0.024474998 #> [6,] -0.32021399 0.375870760 -0.063801457 #> [7,] -0.26743938 0.315515045 -0.065189319 #> [8,] -0.24232885 0.251647367 -0.046310624 #> [9,] -0.32164760 0.193513367 -0.023749200 #> [10,] 0.08909523 -0.042652668 -0.003927533 #> #> $delta0 #> [,1] [,2] [,3] [,4] [,5] #> [1,] 0.98019809 0.0359874961 0.0286611723 -0.0771057946 -0.125123839 #> [2,] 0.03598750 1.0147448520 0.0682717783 -0.0050458661 -0.094050536 #> [3,] 0.02866117 0.0682717783 0.9421324579 -0.0008629448 -0.006328672 #> [4,] -0.07710579 -0.0050458661 -0.0008629448 1.1688360761 0.009587066 #> [5,] -0.12512384 -0.0940505359 -0.0063286722 0.0095870656 1.118850632 #> [6,] -0.07451806 0.0410632195 0.0305856073 -0.0669929721 -0.121122501 #> [7,] 0.12225097 0.0973080058 0.0358317375 -0.0636431219 -0.093537678 #> [8,] -0.19258948 -0.0097150755 0.0094974025 -0.0225974007 -0.025678978 #> [9,] -0.07994959 -0.0006985061 -0.0311627378 -0.0107939039 0.083937298 #> [10,] -0.09886478 0.0160550718 -0.0933971551 0.1175286300 -0.085419906 #> [,6] [,7] [,8] [,9] [,10] #> [1,] -0.074518056 0.12225097 -0.192589481 -0.0799495873 -0.098864777 #> [2,] 0.041063220 0.09730801 -0.009715075 -0.0006985061 0.016055072 #> [3,] 0.030585607 0.03583174 0.009497403 -0.0311627378 -0.093397155 #> [4,] -0.066992972 -0.06364312 -0.022597401 -0.0107939039 0.117528630 #> [5,] -0.121122501 -0.09353768 -0.025678978 0.0839372982 -0.085419906 #> [6,] 0.796628840 0.07131054 -0.029249920 -0.0014254089 0.149911922 #> [7,] 0.071310537 1.09345442 -0.120894064 0.1168935709 0.010947882 #> [8,] -0.029249920 -0.12089406 0.939712239 0.0173921549 -0.001945888 #> [9,] -0.001425409 0.11689357 0.017392155 1.0371615899 0.003445914 #> [10,] 0.149911922 0.01094788 -0.001945888 0.0034459141 1.105870679 #>