FLhd {phd}

Freedman-Lane HD

Description

Provides a class of tests for testing in high-dimensional linear models. The tests are robust against heteroscedasticity and non-normality. They often provide good type I error control even under anti-sparsity.

Usage

  FLhd(y,X,X1,nperm=2E4,lambda="lambda.min",flip="FALSE",nfolds=10,statistic="partialcor")

Arguments

y

The values of the outcome.

X

The design matrix. If the covariate of interest is included in X, it should be included in the first column. If it is not included in X, then specify X1. The data do not need to be standardized, since this is automatically done by this function. Do not include a columns of 1's.

X1

n-vector with the (1-dimensional) covariate of interest. X1 should only be specified if the covariate of interest is not already included in X.

nperm

The number of random permutations (or sign-flipping maps) used by the test

lambda

The penalty used in the ridge regressions. Default is "lambda.min", which means that the penalty is obtained using cross-validation. One can also enter "lambda.1se", which is an upward-conservative estimate of the optimal lambda.

flip

Default is "FALSE", which means that permutation is used. If "TRUE", then sign-flipping is used.

statistic

The type of statistic that is used within the permutation test. Either the partial correlation ("partialcor") r the semi-partia correlation ("semipartialcor").

nfolds

The number of folds used in the cross-validation (in case lambda is determined using cross-validation).

Value

A two-sided p-value.

Examples

set.seed(5193)
n=30

X <- matrix(nr=n,nc=60,rnorm(n*60)) 
y <- X[,1]+X[,2]+X[,3] + rnorm(n,mean=0)   #H0: first coefficient=0. So H0 is false

FLhd(y, X,  nperm=2000, lambda=100,flip="FALSE", statistic="partialcor")