stat.lasso_lambdasmax {knockoff}

Penalized linear regression statistics for knockoff

Description

Computes the signed maximum statistic

W_j = \max(Z_j, \tilde{Z}_j) \cdot \mathrm{sgn}(Z_j - \tilde{Z}_j),

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

Usage

stat.lasso_lambdasmax(X, X_k, y, ...)

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 or lars (see Details).

Details

This function uses glmnet to compute the regularization path on a fine grid of \lambda's.

The additional nlambda parameter can be used to control the granularity of the grid of \lambda values. 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).

This function is a wrapper around the more general stat.glmnet_lambdadiff.

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

Value

A vector of statistics W of length p.

Examples

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, knockoff=knockoffs,
                           statistic=stat.lasso_lambdasmax)
print(result$selected)

# Advanced usage with custom arguments
foo = stat.lasso_lambdasmax
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)