Estimate Dimension of the Sufficient Reduction.
This function estimates the dimension, i.e. the rank of B. The default
method 'CV' performs leave-one-out (LOO) cross-validation using
mars as follows for 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 the space that is orthogonal to the column space of the
CVE estimate of B_k. Method 'wilcoxon' finds the minimum using
the Wilcoxon test.
predict_dim(object, ..., method = "CV")
A list with
criterion for method and k = min.dim, ..., max.dim.
estimated dimension is the minimizer of the 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)
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