optimal_rerandomization_tail_approx: Find the Optimal Rerandomization Design Under the Tail and...
In OptimalRerandExpDesigns: Optimal Rerandomization Experimental Designs

Description Usage Arguments Value Author(s) Examples

Finds the optimal rerandomization threshold based on a user-defined quantile and kurtosis based on an approximation of tail standard errors

optimal_rerandomization_tail_approx(
  W_base_object,
  estimator = "linear",
  q = 0.95,
  c_val = NULL,
  skip_search_length = 1,
  binary_search = FALSE,
  excess_kurtosis_z = 0,
  use_frob_norm_sq_unbiased_estimator = TRUE,
  frob_norm_sq_bias_correction_min_samples = 10,
  smoothing_degree = 1,
  smoothing_span = 0.1,
  dot_every_x_iters = 100
)

`W_base_object`	An object that contains the assignments to begin with sorted by imbalance.
`estimator`	"linear" for the covariate-adjusted linear regression estimator (default).
`q`	The tail criterion's quantile of MSE over z's. The default is 95%.
`c_val`	The c value used (see Equation 8 in the paper). The default is `NULL` corresponding to `qnorm(q)`.
`skip_search_length`	In the exhaustive search, how many designs are skipped? Default is 1 for full exhaustive search through all assignments provided for in `W_base_object`.
`binary_search`	If `TRUE`, a binary search is employed to find the optimal threshold instead of an exhaustive search. Default is `FALSE`.
`excess_kurtosis_z`	An estimate of the excess kurtosis in the measure on z. Default is 0.
`use_frob_norm_sq_unbiased_estimator`	If `TRUE`, this would use the debiased Frobenius norm estimator instead of the naive. Default is `TRUE`.
`frob_norm_sq_bias_correction_min_samples`	The bias-corrected estimate suffers from high variance when there are not enough samples. Thus, we only implement the correction beginning at this number of vectors. Default is 10 and this parameter is only applicable if `use_frob_norm_sq_unbiased_estimator` is `TRUE`.
`smoothing_degree`	The smoothing degree passed to `loess`.
`smoothing_span`	The smoothing span passed to `loess`.
`dot_every_x_iters`	Print out a dot every this many iterations. The default is 100. Set to `NULL` for no printout.

A list containing the optimal design threshold, strategy, and other information.

Adam Kapelner

 
 n = 100
 p = 10
 X = matrix(rnorm(n * p), nrow = n, ncol = p)
 X = apply(X, 2, function(xj){(xj - mean(xj)) / sd(xj)})
 S = 25000
 
 W_base_obj = generate_W_base_and_sort(X, max_designs = S)
 design = optimal_rerandomization_tail_approx(W_base_obj, 
				skip_search_length = 10)
 design