# mvnorm.l2boost: multivariate normal data simulations. In ehrlinger/l2boost: Exploring Friedman's Boosting Algorithm for Regularized Linear Regression

## Description

Create simulated dataset from a multivariate normal. Used to recreate data simulations from Ehrlinger and Ishwaran (2012).

## Usage

 ```1 2``` ```mvnorm.l2boost(n = 100, p = 100, beta = NULL, which.beta = NULL, rho = 0) ```

## Arguments

 `n` number of observations `p` number of coordinate directions in the design matrix `beta` a "true" beta vector of length p (default=NULL) See details. `which.beta` indicator vector for which beta coefficients to include as signal in simulation (default=NULL) see details `rho` correlation coefficient between coordinate directions

## Details

By default, mvnorm.l2boost creates a data set of n multivariate normal random observations of p covariates (see MASS:mvrnorm). The correlation matrix is constructed with 1 on the diagonals and the correlation coefficient rho on the off diagonals.

The response is constructed as follows: If a true beta vector is not supplied, the first 10 beta coefficients carry the signal with a value of 5, and the remaining p-10 values are set to zero. Given a beta.true vector, all values are used as specified. The coefficent vector is truncated to have p signal terms if length(beta.true) > p, and noise coordinates are added if length(beta.true) < p.

It is possible to pass an indicator vector which.beta to select specific signal elements from the full vector beta.true.

## Value

• call Matched function call

• x design matrix of size n x p

• y response vector of length n

## References

Ehrlinger J., and Ishwaran H. (2012). "Characterizing l2boosting" Ann. Statist., 40 (2), 1074-1101

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```#-------------------------------------------------------------------------- # Example: Multivariate normal data simulation # Create a (reproducable) data set of size 100 x 100 set.seed(1024) n<- 100 p<- 100 # Set 10 signal variables using a uniform beta=5, the remaining (p-10)=90 are # set to zero indicating random noise. beta <- c(rep(5,10), rep(0,p-10)) # Example with orthogonal design matrix columns (orthogonal + noise) ortho.data <- mvnorm.l2boost(n, p, beta) cbind(ortho.data\$y[1:5],ortho.data\$x[1:5,]) # Example with correlation between design matrix columns corr.data <- mvnorm.l2boost(n, p, beta, rho=0.65) cbind(corr.data\$y[1:5],corr.data\$x[1:5,]) ```

ehrlinger/l2boost documentation built on May 16, 2019, 1:20 a.m.