penalty | R Documentation |
Calculate the penalty function for estimators selection.
penalty(Delta, n, p, K)
Delta |
vector with |
n |
integer : number of observatons. |
p |
integer : number of variables. |
K |
scalar : constant in the penalty function. |
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))
The values of the penalty function greater than 1e+08 are set to 1e+08.
If for some Delta(d)
the
equation \phi
(x) = exp(-Delta(d)/(d+1))
has no
solution, then the execution is stopped.
Yannick Baraud, Christophe Giraud, Sylvie Huet
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