ridge.proj: P-values based on ridge projection method
In hdi: High-Dimensional Inference

Description Usage Arguments Value Author(s) References Examples

Compute p-values for lasso-type regression coefficients based on the ridge projection method.

ridge.proj(x, y, family = "gaussian", standardize = TRUE,
           lambda = 1, betainit = "cv lasso", sigma = NULL,
           suppress.grouptesting = FALSE,
           multiplecorr.method = "holm", N = 10000)

`x`	design matrix (without intercept).
`y`	response vector.
`family`	family
`standardize`	Should design matrix be standardized to unit column standard deviation (logical)?
`lambda`	Value of penalty parameter lambda (ridge regression).
`betainit`	Either a numeric vector, corresponding to a sparse estimate of the coefficient vector, or the method to be used for the initial estimation, "scaled lasso" or "cv lasso".
`sigma`	Estimate of the standard deviation of the error term. This estimate needs to be compatible with the initial estimate (see betainit) provided or calculated. Otherwise, results won't be correct.
`suppress.grouptesting`	A boolean to optionally suppress the preparations made for testing groups. This will avoid quite a bit of computation and memory usage. The output will also be smaller.
`multiplecorr.method`	Either "WY" or any of `p.adjust.methods`.
`N`	number of empirical samples (only used if `multiplecorr.method = "WY"`).

`pval`	Individual p-values for each parameter.
`pval.corr`	Multiple testing corrected p-values for each parameter.
`groupTest`	Function to perform groupwise tests. Groups are indicated using an index vector with entries in {1,…,p} or a list thereof.
`clusterGroupTest`	Function to perform groupwise tests based on hierarchical clustering. You can either provide a distance matrix and clustering method or the output of hierarchical clustering from the function `hclust` as for `clusterGroupBound`. P-values are adjusted for multiple testing.

sigmahat

sigma coming from the scaled lasso.

Peter Buehlmann, Ruben Dezeure, Lukas Meier

Bühlmann, P. (2013) Statistical significance in high-dimensional linear models. Bernoulli 19, 1212–1242.

x <- matrix(rnorm(100 * 100), nrow = 100, ncol = 100)
y <- x[,1] + x[,2] + rnorm(100)
fit.ridge <- ridge.proj(x, y)
which(fit.ridge$pval.corr < 0.05)

## Use the scaled lasso for the initial estimate
fit.ridge.scaled  <- ridge.proj(x, y, betainit = "scaled lasso")
which(fit.ridge.scaled$pval.corr < 0.05)

## Group-wise testing of the first two coefficients
fit.ridge$groupTest(1:2)

## Hierarchical testing using distance matrix based on
## correlation matrix
out.clust <- fit.ridge$clusterGroupTest()
plot(out.clust)

## Fit the method without doing the preparations
## for group testing (saves time and memory)
fit.ridge.faster <- ridge.proj(x, y, suppress.grouptesting = TRUE)