optimize_mse function

Optimize MSE of LNC Estimator

Gaussian process (GP) optimization is used to minimize the MSE of the LNC estimator with respect to the non-uniformity threshold parameter alpha. A normal distribution with compound-symmetric covariance is used as a reference distribution to optimize the MSE of LNC with respect to.

optimize_mse(rho, N, M, d, k, lower = -10, upper = -1e-10,
  num_iter = 10, init_size = 20, cluster = NULL, verbose = TRUE)

Arguments

• rho: Reference correlation.
• N: Sample size.
• M: Number of replications.
• d: Dimension.
• k: Neighborhood order.
• lower: Lower bound for optimization.
• upper: Upper bound for optimization.
• num_iter: Number of iterations of GP optimization.
• init_size: Number of initial evaluation to estimating GP.
• cluster: A parallel cluster object.
• verbose: If TRUE then print runtime diagnostic output.

Details

The package tgp is used to fit a treed-GP to the MSE estimates of LNC. A treed-GP is used because the MSE of LNC with respect to alpha exhibits clear non-stationarity. A treed-GP is able to identify the function's different correlation lengths which improves optimization.