predict_dim {CVE}R Documentation

Estimate Dimension of Reduction Space.

Description

This function estimates the dimension of the mean dimension reduction space, i.e. number of columns of B matrix. The default method 'CV' performs l.o.o cross-validation using mars. Given k = min.dim, ..., max.dim a cross-validation via mars is performed on the dataset (Y_i, B_k' X_i)_{i = 1, ..., n} where B_k is the p x k dimensional CVE estimate. The estimated SDR dimension is the k where the cross-validation mean squared error is minimal. The method 'elbow' estimates the dimension via k = argmin_k L_n(V_{p - k}) where V_{p - k} is space that is orthogonal to the columns-space of the CVE estimate of B_k. Method 'wilcoxon' is similar to 'elbow' but finds the minimum using the wilcoxon-test.

Usage

predict_dim(object, ..., method = "CV")

Arguments

object

an object of class "cve", usually, a result of a call to cve or cve.call.

...

ignored.

method

This parameter specify which method will be used in dimension estimation. It provides three methods 'CV' (default), 'elbow', and 'wilcoxon' to estimate the dimension of the SDR.

Value

list with

cretirion of method for k = min.dim, ..., max.dim.

k

estimated dimension as argmin over k of criterion.

Examples

# create B for simulation
B <- rep(1, 5) / sqrt(5)

set.seed(21)
# creat predictor data x ~ N(0, I_p)
x <- matrix(rnorm(500), 100)

# simulate response variable
#    y = f(B'x) + err
# with f(x1) = x1 and err ~ N(0, 0.25^2)
y <- x %*% B + 0.25 * rnorm(100)

# Calculate cve for unknown k between min.dim and max.dim.
cve.obj.simple <- cve(y ~ x) 

predict_dim(cve.obj.simple)


[Package CVE version 0.2 Index]