optimal_rerandomization_tail_approx {OptimalRerandExpDesigns}

Find the Optimal Rerandomization Design Under the Tail and Kurtosis Approximation

Description

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

Usage

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
)

Arguments

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.

Value

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

Author(s)

Adam Kapelner

Examples

 
 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