estimate_mse function

Estimate MSE of LNC Estimator

Computes the MSE of the Local Non-Uniformity Correct (LNC) KSG estimator for a given value of the tuning parameter alpha, dimension, neighborhood order, and sample size.

estimate_mse(k = 5, alpha = 0, d = 2, rho = 0, N = 1000,
  M = 100, cluster = NULL)

Arguments

• k: Neighborhood order.
• alpha: Non-uniformity threshold (see details).
• d: Dimension.
• rho: Reference correlation (see details).
• N: Sample size.
• M: Number of replications.
• cluster: A parallel cluster object.

Details

The parameter alpha controls the threshold for the application of the non-uniformity correction to a particular point's neighborhood. Roughly, alpha is the ratio of the PCA aligned neighborhood volume to the rectangular aligned neighborhood volume below which indicates non-uniformity and the correction is applied.

If alpha < 0 then a log scale is assumed; otherwise [0,1] scale is used. alpha > 1 are unacceptable values. A value of alpha = 0 forces no correction and LNC reverts to the KSG estimator.

The reference distribution that is assumed is a mean-zero multivariate normal distribution with a compound-symmetric covariance. The covariance matrix has a single correlation parameter supplied by rho.

Examples

estimate_mse(N = 100,M = 2)