Knockoff filter forward selection statistics

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Description

Computes the statistic

W_j = \max(Z_j, Z_{j+p}) \cdot \mathrm{sgn}(Z_j - Z_{j+p}),

where Z_1,…,Z_{2p} give the reverse order in which the 2p variables (the originals and the knockoffs) enter the forward selection model. See the Details for information about forward selection.

Usage

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knockoff.stat.fs(X, X_ko, y)

knockoff.stat.fs_omp(X, X_ko, y)

Arguments

X

original design matrix

X_ko

knockoff matrix

y

response vector

Details

In forward selection, the variables are chosen iteratively to maximize the inner product with the residual from the previous step. The initial residual is always y. In standard forward selection (knockoff.stats.fs), the next residual is the remainder after regressing on the selected variable; when orthogonal matching pursuit is used (knockoff.stats.fs_omp), the next residual is the remainder after regressing on all the previously selected variables.

Value

The statistic W