standardize: Standardization of High-Dimensional Design Matrices

In statcodes/SIS: Sure Independence Screening

Standardization of High-Dimensional Design Matrices

Description

Standardizes the columns of a high-dimensional design matrix to mean zero and unit Euclidean norm.

Usage

standardize(X)

Arguments

X	A design matrix to be standardized.

Details

Performs a location and scale transform to the columns of the original design matrix, so that the resulting design matrix with p-dimensional observations \{x_i : i=1,...,n\} of the form x_i=(x_{i1},x_{i2},...,x_{ip}) satisfies \sum_{i=1}^{n} x_{ij} = 0 and \sum_{i=1}^{n} x_{ij}^{2} = 1 for j=1,...,p.

Value

A design matrix with standardized predictors or columns.

Author(s)

Jianqing Fan, Yang Feng, Diego Franco Saldana, Richard Samworth, and Yichao Wu

References

Diego Franco Saldana and Yang Feng (2018) SIS: An R package for Sure Independence Screening in Ultrahigh Dimensional Statistical Models, Journal of Statistical Software, 83, 2, 1-25.

Examples

## Not run: 
set.seed(0)
n <- 400
p <- 50
rho <- 0.5
corrmat <- diag(rep(1 - rho, p)) + matrix(rho, p, p)
corrmat[, 4] <- sqrt(rho)
corrmat[4, ] <- sqrt(rho)
corrmat[4, 4] <- 1
corrmat[, 5] <- 0
corrmat[5, ] <- 0
corrmat[5, 5] <- 1
cholmat <- chol(corrmat)
x <- matrix(rnorm(n * p, mean = 15, sd = 9), n, p)
x <- x %*% cholmat

x.standard <- standardize(x)

## End(Not run)

statcodes/SIS documentation built on March 31, 2024, 6:57 p.m.