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

In EDR: Estimation of the Effective Dimension Reduction ('EDR') Space

Description

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

Usage

## S3 method for class '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

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 Λ V^T

and the distance specified by Li (1992) are computed.

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).

Author(s)

Joerg Polzehl, [e-mail]

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

require(EDR)
## Not run: demo(edr_ex1)
## Not run: demo(edr_ex2)

Example output

Loading required package: sm
Package 'sm', version 2.2-5.4: type help(sm) for summary information

EDR documentation built on March 26, 2020, 8:42 p.m.