Calculate the penalty function for estimators selection.
penalty(Delta, n, p, K)A vector with the same length as Delta: for each d=0, ..., Dmax, let
N=n-d, D=d+1 and
pen(d) = x K N/(N-1) where x satisfies
\(\phi\)(x) = exp(-Delta(d)), when Delta(d)<50,
where \(\phi\)(x)=pf(q=x/(D+2),df1=D+2,df2=N-1,lower.tail=F)-(x/D)pf(q=(N+1)x/D(N-1),df1=D,df2=N+1,lower.tail=F)
\(\psi\)(x) = Delta(d), when
Delta(d)\(\ge\)50,
where \(\psi\)(x)=lbeta(1+D/2,(N-1)/2)-log(2(2x+(N-1)D)/((N-1)(N+2)x))-(N-1)/2log((N-1)/(N-1+x))-(D/2)log(x/(N-1+x))
vector with Dmax+1 components : weights in the penalty function.
integer : number of observatons.
integer : number of variables.
scalar : constant in the penalty function.
Yannick Baraud, Christophe Giraud, Sylvie Huet