EDR (version 0.6-6)

summary.edr: Summary information for objects produced by function edr.

Description

The function provides information on the estimated effective dimension reduction (EDR) space.

Usage

# S3 method for edr
summary(object, m = 1, R = NULL, ...)

Arguments

object

Object of class "edr".

m

Dimension of the effective dimension reduction (EDR) space. m=1 corresponds to single index models, m>1 specifies a multiindex model. Determines the number of eigenvectors and cumulative eigenvalues to show.

R

If code R specifies a matrix (dimension c(k,d), \(k>=m\), d=dim(object$x)[2], this matrix is interpreted as spanning the true EDR space. Two distances between the estimated EDR space and the space spanned R[1:m,] are computed.

...

Additional parameters will be ignored

Value

Returns a list with components

Rhat

(First) m eigenvectors of the estimated EDR space.

cumlam

Cummulative sum of first m eigenvalues of object$bhat, standardized by the sum of all eigenvalues.

loss1

If R was specified the distance \(||R (I- \hat{P}_m)||/||R||\) between the true and estimated m-dimensional EDR space.

loss2

The distance specified by Li (1992).

Details

Provides information on the estimated effective dimension reduction (EDR) space. The first m basis vectors and the cummulative sum of normalized eigenvalues of matrix object$bhat are given. If R is specified the distance $$||R (I- \hat{P}_m)||/||R|| \mbox{with} \hat{P}_m = U_m^T U_m , \hat{R}_m=U_m \Lambda V^T $$ and the distance specified by Li (1992) are computed.

References

M. Hristache, A. Juditsky, J. Polzehl and V. Spokoiny (2001). Structure adaptive approach for dimension reduction, The Annals of Statistics. Vol.29, pp. 1537-1566. \ J. Polzehl, S. Sperlich (2009). A note on structural adaptive dimension reduction, J. Stat. Comput. Simul.. Vol. 79 (6), pp. 805--818. \ K.-C. Li (1992). On principal Hessian directions for data visualization and dimension reduction: another application of Stein's lemma, JASA, Vol. 87, pp. 1025-1039.

See Also

edr, edr.R, print.edr, plot.edr

Examples

# NOT RUN {
require(EDR)
# }
# NOT RUN {
demo(edr_ex1)
# }
# NOT RUN {
demo(edr_ex2)
# }