# simulData: simulData In LINselect: Selection of Linear Estimators

## Description

Function to simulate data Y = X β + σ N(0, 1)

## Usage

 ```1 2``` ```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 ≤ a, b ≤ 15
`C[a,b] = r**abs(a-b)` for 16 ≤ a, b ≤ 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 β divided by `rSN*n`.

## Value

A list with components :

 `Y` vector `n` : Y = X β + σ 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

LINselect documentation built on Jan. 10, 2020, 9:08 a.m.