predict_dim {CVE} | R Documentation |
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.
predict_dim(object, ..., method = "CV")
object |
an object of class |
... |
ignored. |
method |
This parameter specify which method will be used in dimension
estimation. It provides three methods |
list with
cretirion of method for k = min.dim, ..., max.dim
.
estimated dimension as argmin over k of criterion.
# 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)