Function to simulate data \(Y = X \beta + \sigma N(0, 1)\)
simulData(p = 100, n = 100, beta = NULL, C = NULL, r = 0.95,
rSN = 10)A list with components :
vector n : \(Y = X \beta + \sigma N(0, 1)\)
matrix n x p : values of the covariates. See
details.
matrix p x p. See details
scalar. See details.
vector with p components. See details.
integer : number of variates. Should be >15 if beta=NULL
integer : number of observations
vector with p components. See details.
matrix p x p. Covariance matrix of X. See details.
scalar for calculating the covariance of X when C=NULL.
scalar : ratio signal/noise
Yannick Baraud, Christophe Giraud, Sylvie Huet
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.