LINselect (version 1.1.5)

simulData: simulData

Description

Function to simulate data $Y=X\beta +\sigma N(0,1)$

Usage

simulData(p = 100, n = 100, beta = NULL, C = NULL, r = 0.95, 
    rSN = 10)

Value

A list with components :

Y

vector n : $Y=X\beta +\sigma N(0,1)$

X

matrix n x p : values of the covariates. See details.

C

matrix p x p. See details

sigma

scalar. See details.

beta

vector with p components. See details.

Arguments

p

integer : number of variates. Should be >15 if beta=NULL

n

integer : number of observations

beta

vector with p components. See details.

C

matrix p x p. Covariance matrix of X. See details.

r

scalar for calculating the covariance of X when C=NULL.

rSN

scalar : ratio signal/noise

Author

Yannick Baraud, Christophe Giraud, Sylvie Huet

Details

When beta is NULL, then p should be greater than 15 and beta=c(rep(2.5,5),rep(1.5,5),rep(0.5,5),rep(0,p-15))

When C is NULL, then C is block diagonal with
C[a,b] = r**abs(a-b) for $1\le a,b\le 15$
C[a,b] = r**abs(a-b) for $16\le a,b\le p$

The lines of X are n i.i.d. gaussian variables with mean 0 and covariance matrix C.

The variance sigma**2 equals the squared euclidean norm of $X\beta$ divided by rSN*n.