# LASSO.fit.nonpen: LASSO Penalized Quantile Regression with some nonpenalized... In rqPen: Penalized Quantile Regression

## Description

LASSO.fit.nonpen obtains coefficient estimates for Lasso penalized quantile regression with some nonpenalized coefficients. It is called by the QICD.nonpen function to obtain initial estimates when they are not provided.

## Usage

 `1` ```LASSO.fit.nonpen(y, x, z, tau, lambda, intercept, coef.cutoff, weights=NULL) ```

## Arguments

 `y` Vector of responses. `x` n x p matrix of covariates. `z` n x q matrix of observations with each row corresponding to one observation. Penalties (and variable selection) WILL NOT be applied to these coefficients. Do not include column of 1's; set intercept=TRUE, if intercept is desired. `tau` Conditional quantile being modelled. `lambda` Tuning parameter. Must be positive. `intercept` If TRUE, an intercept is included in the model. If FALSE, no intercept is included. `coef.cutoff` Coefficients with magnitude less than this value are set to 0. `weights` If not NULL, weights must be a vector of length n with a positive weight for each observation. This is used for the linear programming solution for the SCAD and MCP penalties.

## Details

This is a barebones function that only provides coefficient estimates. It will not provide any warnings or errors, so you need to check that inputs are accurate and appropriate. The rq.lasso.fit function should be used to obtain more information from the Lasso fit.

## Value

Returns a vector containing the intercept (if intercept=TRUE) and the estimated coefficients for each column in x and z.

Adam Maidman

## References

 Tibshirani, R. (1996). Regression shrinkage and selection via the lasso. Journal of the Royal Statistical Society. Series B, 58, 267–288.

## Examples

 ```1 2 3 4 5 6 7 8 9``` ```library(splines) n = 50 p = 100 x <- matrix(rnorm(n*p),nrow=n) z1 <- runif(n) z <- bs(z1) y <- 0 + x[,1] - 3*x[,5] + z1^3 + rnorm(n) fit1 <- LASSO.fit.nonpen(y,x,z, tau=.5, lambda=1, intercept=TRUE, coef.cutoff=1e-08) fit2 <- LASSO.fit.nonpen(y,x,z, tau=.5, lambda=.1, intercept=TRUE, coef.cutoff=1e-08) ```

rqPen documentation built on April 14, 2020, 7:14 p.m.