# rq.fit.lasso: Lasso Penalized Quantile Regression In quantreg: Quantile Regression

## Description

The fitting method implements the lasso penalty of Tibshirani for fitting quantile regression models. When the argument `lambda` is a scalar the penalty function is the l1 norm of the last (p-1) coefficients, under the presumption that the first coefficient is an intercept parameter that should not be subject to the penalty. When `lambda` is a vector it should have length equal the column dimension of the matrix `x` and then defines a coordinatewise specific vector of lasso penalty parameters. In this case `lambda` entries of zero indicate covariates that are not penalized. There should be a sparse version of this, but isn't (yet).

## Usage

 `1` ```rq.fit.lasso(x, y, tau = 0.5, lambda = 1, beta = .9995, eps = 1e-06) ```

## Arguments

 `x` the design matrix `y` the response variable `tau` the quantile desired, defaults to 0.5. `lambda` the value of the penalty parameter(s) that determine how much shrinkage is done. This should be either a scalar, or a vector of length equal to the column dimension of the `x` matrix. `beta` step length parameter for Frisch-Newton method. `eps` tolerance parameter for convergence.

## Value

Returns a list with a coefficient, residual, tau and lambda components. When called from `"rq"` (as intended) the returned object has class "lassorqs".

R. Koenker

## References

Koenker, R. (2005 Quantile Regression, CUP.

`rq`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```n <- 60 p <- 7 rho <- .5 beta <- c(3,1.5,0,2,0,0,0) R <- matrix(0,p,p) for(i in 1:p){ for(j in 1:p){ R[i,j] <- rho^abs(i-j) } } set.seed(1234) x <- matrix(rnorm(n*p),n,p) %*% t(chol(R)) y <- x %*% beta + rnorm(n) f <- rq(y ~ x, method="lasso",lambda = 30) g <- rq(y ~ x, method="lasso",lambda = c(rep(0,4),rep(30,4))) ```

### Example output

```Loading required package: SparseM

Attaching package: 'SparseM'

The following object is masked from 'package:base':

backsolve
```

quantreg documentation built on Feb. 3, 2018, 1:03 a.m.