| summary.edr {EDR} | R Documentation |
The function provides information on the estimated effective dimension reduction (EDR) space.
summary.edr(object, m = 1, R = NULL, ...)
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$x)[2], this matrix is interpreted as spanning the true
EDR space. Two distances between the estimated EDR space and the space spanned
R[1:m,] are computed. |
... |
Additional parameters will be ignored |
Provides information on the estimated effective dimension reduction (EDR) space.
The first m basis vectors and the cummulative sum of normalized eigenvalues of matrix
object$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.
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). |
Joerg Polzehl, polzehl@wias-berlin.de
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.
edr, edr.R, print.edr, plot.edr
require(EDR) ## Not run: demo(edr_ex1) ## Not run: demo(edr_ex2)