# FLhd: Freedman-Lane HD In phd: Permutation Testing in High-Dimensional Linear Models

## 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

 `1` ``` 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

 ```1 2 3 4 5 6 7``` ```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") ```

phd documentation built on Jan. 6, 2022, 1:06 a.m.