# stat.lasso_lambdadiff: Importance statistics based on the lasso In knockoff: The Knockoff Filter for Controlled Variable Selection

## Description

Fit the lasso path and computes the difference statistic

W_j = Z_j - \tilde{Z}_j

where Z_j and \tilde{Z}_j are the maximum values of the regularization parameter λ at which the jth variable and its knockoff enter the penalized linear regression model, respectively.

## Arguments

 X n-by-p matrix of original variables. X_k n-by-p matrix of knockoff variables. y vector of length n, containing the response variables. It should be numeric. ... additional arguments specific to glmnet (see Details).

## Details

This function uses glmnet to compute the lasso path on a fine grid of λ's and is a wrapper around the more general stat.glmnet_lambdadiff.

The nlambda parameter can be used to control the granularity of the grid of λ's. The default value of nlambda is 500.

Unless a lambda sequence is provided by the user, this function generates it on a log-linear scale before calling glmnet (default 'nlambda': 500).

For a complete list of the available additional arguments, see glmnet or lars.

## Value

A vector of statistics W of length p.

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 p=200; n=100; k=15 mu = rep(0,p); Sigma = diag(p) X = matrix(rnorm(n*p),n) nonzero = sample(p, k) beta = 3.5 * (1:p %in% nonzero) y = X %*% beta + rnorm(n) knockoffs = function(X) create.gaussian(X, mu, Sigma) # Basic usage with default arguments result = knockoff.filter(X, y, knockoffs=knockoffs, statistic=stat.lasso_lambdadiff) print(result$selected) # Advanced usage with custom arguments foo = stat.lasso_lambdadiff k_stat = function(X, X_k, y) foo(X, X_k, y, nlambda=200) result = knockoff.filter(X, y, knockoffs=knockoffs, statistic=k_stat) print(result$selected)