r4: Robust reduced-rank regression

In rrpack: Reduced-Rank Regression

Robust reduced-rank regression

Description

Perform robust reduced-rank regression.

Usage

r4(
  Y,
  X,
  maxrank = min(dim(Y), dim(X)),
  method = c("rowl0", "rowl1", "entrywise"),
  Gamma = NULL,
  ic.type = c("AIC", "BIC", "PIC"),
  modstr = list(),
  control = list()
)

Arguments

Y	a matrix of response (n by q)
X	a matrix of covariate (n by p)
maxrank	maximum rank for fitting
method	outlier detection method, either entrywise or rowwise
Gamma	weighting matrix in the loss function
ic.type	information criterion, AIC, BIC or PIC
modstr	a list of model parameters controlling the model fitting
control	a list of parameters for controlling the fitting process

Details

The model parameters can be controlled through argument modstr. The available elements include

• nlam: parameter in the augmented Lagrangian function.

• adaptive: if TRUE, use leverage values for adaptive penalization. The default value is FALSE.

• weights: user supplied weights for adaptive penalization.

• minlam: maximum proportion of outliers.

• maxlam: maximum proportion of good observations.

• delid: discarded observation indices for initial estimation.

The model fitting can be controlled through argument control. The available elements include

• epsilon: convergence tolerance.

• maxit: maximum number of iterations.

• qr.tol: tolerance for qr decomposition.

• tol: tolerance.

Value

a list consisting of

coef.path	solutuon path of regression coefficients
s.path	solutuon path of sparse mean shifts
s.norm.path	solutuon path of the norms of sparse mean shifts
ic.path	paths of information criteria
ic.smooth.path	smoothed paths of information criteria
lambda.path	paths of the tuning parameter
id.solution	ids of the selected solutions on the path
ic.best	lowest values of the information criteria
rank.best	rank values of selected solutions
coef	estimated regression coefficients
s	estimated sparse mean shifts
rank	rank estimate

References

She, Y. and Chen, K. (2017) Robust reduced-rank regression. Biometrika, 104 (3), 633–647.

Examples

## Not run: 
library(rrpack)
n <- 100; p <- 500; q <- 50
xrank <- 10; nrank <- 3; rmax <- min(n, p, q, xrank)
nlam <- 100; gamma <- 2
rho_E <- 0.3
rho_X <- 0.5
nlev <- 0
vlev <- 0
vout <- NULL
vlevsd <- NULL
nout <- 0.1 * n
s2n <- 1
voutsd <- 2
simdata <- rrr.sim5(n, p, q, nrank, rx = xrank, s2n = s2n,
                    rho_X = rho_X, rho_E = rho_E, nout = nout, vout = vout,
                    voutsd = voutsd,nlev = nlev,vlev=vlev,vlevsd=vlevsd)
Y <- simdata$Y
X <- simdata$X
fit <- r4(Y, X, maxrank = rmax,
               method = "rowl0", ic.type= "PIC")
summary(fit)
coef(fit)
which(apply(fit$s,1,function(a)sum(a^2))!=0)

## End(Not run)

rrpack documentation built on June 16, 2022, 9:05 a.m.