edrcv {EDR} | R Documentation |
Tis function, additionally to estimating the
effective dimension reduction space (EDR), see also function edr
, estimates the Mean Squared Error of Prediction (MSEP) and the Mean Absolute Error of Prediction (MAEP) when using the estimated EDR by Cross-Validation. Estimates of the regression function are produced using function sm.regression
from package sm
.
edrcv(x, y, m = 2, rho0 = 1, h0 = NULL, ch = exp(0.5/max(4, (dim(x)[2]))), crhomin = 1, cm = 4, method = "Penalized", basis = "Quadratic", cw = NULL, graph = FALSE, show = 1, trace = FALSE, seed = 1, cvsize = 1, m0 = min(m, 2),hsm=NULL)
x |
x specifies the design matrix, dimension (n,d) |
y |
y specifies the response, length n . |
m |
Rank of matrix M in case of method="Penalized" , not used for the other methods. |
rho0 |
Initial value for the regularization parameter rho. |
h0 |
Initial bandwidth. |
ch |
Factor for indecreasing h with iterations. |
crhomin |
Factor to in(de)crease the default value of rhomin. This is just added to explore properties of the algorithms. Defaults to 1. |
cm |
Factor in the definition of Pi_k=C_m*rho_k^2 I_L + hat{M}_{k-1}. Only used if method="Penalized" . |
method |
Secifies the algoritm to use. The default method="Penalized" corresponds to the algoritm
proposed in ... (2006). method="HJPS" corresponds to the original algorithm from
Hristache et.al. (2001) while method="HJPS2" specifies a modifification
(correction) of this algoritm.
|
basis |
Specifies the set of basis functions. Options are basis="Quadratic" (default) and basis="Linear" . |
cw |
cw another regularization parameter, secures identifiability of a minimum number of local gradient directions. Defaults to 1/d . Has to be positive or NULL . |
graph |
If graph==TRUE intermediate results are plotted. |
show |
If graph==TRUE the parameter show determines the dimension of the EDR that is to be used when plotting
intermediate results. If trace=TRUE and !is.null(R) it determines the dimension of the EDR when computing
the risk values. |
trace |
trace=TRUE additional diagnostics are provided for each iteration. This includes
current, at iteration k, values of the regularization parameter rho_k and bandwidth h_k,
normalized cimmulative sums of eigenvalues of hat{B} and if !is.null(R) two distances between the
true, specified in R and estimated EDR. |
seed |
Seed for generating random groups for CV |
cvsize |
Groupsize k in leave-k-out CV |
m0 |
Dimension of the dimension reduction space to use when fitting the data. Should be either 1 or 2. |
hsm |
If is.null(hsm) the bandwidth used by sm.regression for smoothing within the EDR is chosen by cross-validation within sm.regression when needed. Alternatively a grid of bandwidths may be specified. In that case a bandwidth for sm.regression is chosen from the grid that minimizes the extimated mean absolute error of prediction. |
This function performs a leave-k-out cross-validation to estimate the risk
in terms of Mean Squared Error of Prediction (MSEP) and Mean Absolute Error of Prediction (MAEP) when using function edr
to estimate an
effective dimension reduction space of dimension m0
and using this estimated space to predict values of the response. Smoothing within the dimension reduction space is performed using the function sm.regression
from package sm
. The bandwidth for sm.regression
is
chosen by Cross-Validation.
Object of class "edr"
with components.
x |
The design matrix. |
y |
The values of the response. |
bhat |
Matrix hat{B} characterizing the effective dimension space. For a specified dimension m
hat{B}_m = hat{B} O_m, with hat{B}^T hat{B}= O Lambda O^T being the eigenvalue decomposition of hat{B}^T hat{B},
specifies the projection to the m -dimensional subspace that provides the best approximation. |
fhat |
an highly oversmoothed estimate of the values of the regression function at the design points. This is provided
as a backup only for the case that package sm is not installed. |
cumlam |
Cummulative amount of information explained by the first components of hat{B}. |
nmean |
Mean numbers of observations used in each iteration. |
h |
Final bandwidth |
rho |
Final value of rho |
h0 |
Initial bandwidth |
rho0 |
Initial value of rho |
cm |
The factor cm |
call |
Arguments of the call to edrcv |
cvres |
Residuals from cross-validation. |
cvmseofh |
Estimates of MSEP for bandwidths hsm |
cvmaeofh |
Estimates of MAEP for bandwidths hsm |
cvmse |
Estimate of MSEP |
cvmae |
Estimate of MAEP |
hsm |
Set of bandwidths specified for use with sm.regression |
hsmopt |
Bandwidth selected for use with sm.regression if hsm was specified. |
This function requires package sm
.
Joerg Polzehl, polzehl@wias-berlin.de
edr
,plot.edr
, summary.edr
, print.edr
, edr.R
require(EDR) demo(edr_ex4)