r4 {rrpack}

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)