Elbow plot of the loss function.

Description

Boxplots of the output L from cve over k from min.dim to max.dim. For given k, L corresponds to L_n(V, X_i) where V is a stiefel manifold element as minimizer of L_n(V), for further details see Fertl, L. and Bura, E. (2019).

Usage

## S3 method for class 'cve'
plot(x, ...)

Arguments

References

Fertl, L. and Bura, E. (2019), Conditional Variance Estimation for Sufficient Dimension Reduction. Working Paper.

See Also

see par for graphical parameters to pass through as well as plot, the standard plot utility.

Examples

# create B for simulation
B <- cbind(rep(1, 6), (-1)^seq(6)) / sqrt(6)

set.seed(21)
# creat predictor data x ~ N(0, I_p)
X <- matrix(rnorm(600), 100)

# simulate response variable
#    y = f(B'x) + err
# with f(x1, x2) = x1^2 + 2 x2 and err ~ N(0, 0.25^2)
Y <- (X %*% B[, 1])^2 + 2 * X %*% B[, 2] + rnorm(100, 0, .1)

# Create bandwidth estimation function
estimate.bandwidth <- function(X, k, nObs) {
    n <- nrow(X)
    p <- ncol(X)
    X_c <- scale(X, center = TRUE, scale = FALSE)
    2 * qchisq((nObs - 1) / (n - 1), k) * sum(X_c^2) / (n * p)
}
# calculate cve with method 'simple' for k = min.dim,...,max.dim
cve.obj.simple <- cve(Y ~ X, h = estimate.bandwidth, nObs = sqrt(nrow(X)))

# elbow plot
plot(cve.obj.simple)