simulData {LINselect}

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)

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

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.

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.

Note

Library mvtnorm is loaded.

Author(s)

Yannick Baraud, Christophe Giraud, Sylvie Huet