ncl function

fit a nonconvex loss based robust linear model

Fit a linear model via penalized nonconvex loss function.

## S3 method for class 'formula'
ncl(formula, data, weights, offset=NULL, contrasts=NULL, 
x.keep=FALSE, y.keep=TRUE, ...)
## S3 method for class 'matrix'
ncl(x, y, weights, offset=NULL, ...)
## Default S3 method:
ncl(x,  ...)

Arguments

• formula: symbolic description of the model, see details.
• data: argument controlling formula processing via model.frame.
• weights: optional numeric vector of weights. If standardize=TRUE, weights are renormalized to weights/sum(weights). If standardize=FALSE, weights are kept as original input
• x: input matrix, of dimension nobs x nvars; each row is an observation vector
• y: response variable. Quantitative for rfamily="clossR" and -1/1 for classification.
• offset: Not implemented yet
• contrasts: the contrasts corresponding to levels from the respective models
• x.keep, y.keep: For glmreg: logical values indicating whether the response vector and model matrix used in the fitting process should be returned as components of the returned value. For ncl_fit: x is a design matrix of dimension n * p, and x is a vector of observations of length n.
• ...: Other arguments passing to ncl_fit

Details

The robust linear model is fit by majorization-minimization along with linear regression. Note that the objective function is

.

Returns

An object with S3 class "ncl" for the various types of models. - call: the call that produced this object

• fitted.values: predicted values

• h: pseudo response values in the MM algorithm

References

Zhu Wang (2021), MM for Penalized Estimation, TEST, tools:::Rd_expr_doi("10.1007/s11749-021-00770-2")

Author(s)

Zhu Wang zwang145@uthsc.edu

See Also

print, predict, coef.

Examples

#binomial
x=matrix(rnorm(100*20),100,20)
g2=sample(c(-1,1),100,replace=TRUE)
fit=ncl(x,g2,s=1,rfamily="closs")