R: Lasso Penalized Quantile Regression

rq.fit.lasso {quantreg} | R Documentation

## Lasso Penalized 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

    rq.fit.lasso(x, y, tau = 0.5, lambda = 1, beta = .99995, 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".

### Author(s)

R. Koenker

### References

Koenker, R. (2005 Quantile Regression, CUP.

### See Also

`rq`

### Examples

    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)))

[Package quantreg version 5.70 Index]