Description Usage Arguments Details Value Author(s) References See Also Examples
BIC-type criterion for selecting the dimensionality of a dimension reduction subspace.
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object |
a |
plot |
if |
M |
the kernel matrix. See details below. |
x |
the predictors data matrix. See details below. |
type |
See details below. |
nslices |
the number of slices. See details below. |
tol |
a tolerance value |
This BIC-type criterion for the determination of the structural dimension selects d as the maximizer of
G(d) = l(d) - Penalty(p,d,n)
where l(d) is the log-likelihood for dimensions up to d, p is the number of predictors, and n is the sample size. The term Penalty(p,d,n) is the type of penalty to be used:
type = 1
: Penalty(p,d,n) = -(p-d) \log(n)
type = 2
: Penalty(p,d,n) = 0.5 C d (2p-d+1), where C = (0.5 \log(n) + 0.1 n^(1/3))/2 nslices/n
type = 3
: Penalty(p,d,n) = 0.5 C d (2p-d+1), where C = \log(n) nslices/n
type = 4
Penalty(p,d,n) = 1/2 d \log(n)
Returns a list with components:
evalues |
eigenvalues |
l |
log-likelihood |
crit |
BIC-type criterion |
d |
selected dimensionality |
The msir.bic
also assign the above information to the corresponding 'msir'
object.
Luca Scrucca luca.scrucca@unipg.it
Zhu, Miao and Peng (2006) "Sliced Inverse Regression for CDR Space Estimation", JASA.
Zhu, Zhu (2007) "On kernel method for SAVE", Journal of Multivariate Analysis.
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