ncl_fit function

Internal function to fit a nonconvex loss based robust linear model

Fit a linear model via penalized nonconvex loss function.

ncl_fit(x,y, weights, offset=NULL, 
        rfamily=c("clossR", "closs", "gloss", "qloss"), 
        s=NULL, fk=NULL, iter=10, reltol=1e-5, trace=FALSE)

Arguments

• 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 classifications.
• weights: observation weights. Can be total counts if responses are proportion matrices. Default is 1 for each observation
• offset: this can be used to specify an a priori known component to be included in the linear predictor during fitting. This should be NULL or a numeric vector of length equal to the number of cases. Currently only one offset term can be included in the formula.
• rfamily: Response type and relevant loss functions (see above)
• s: nonconvex loss tuning parameter for robust regression and classification.
• fk: predicted values at an iteration in the MM algorithm
• iter: number of iteration in the MM algorithm
• reltol: convergency criteria
• trace: If TRUE, fitting progress is reported

Details

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

.

Returns

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

• 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

ncl