SimBaRepro (version 0.1.0)

confidence_grid: confidence_grid

Description

returns the indicator array

Usage

confidence_grid(
  alpha,
  lower_bds,
  upper_bds,
  seeds,
  generating_fun,
  s_obs,
  tol,
  resolution,
  theta_init = NULL,
  T_stat = ma_depth
)

Value

A list containing an indicator array (ind_array) representing the confidence set, the confidence set lower bounds (updated_lower_bds), and the confidence set upper bounds (updated_upper_bds).

Arguments

alpha

A numeric representing the significance level of the test.

lower_bds

A vector containing the lower bounds for the parameter search space.

upper_bds

A vector containing the upper bounds for the parameter search space.

seeds

A matrix (or array) of seeds for generating artificial statistics.

generating_fun

A function that takes the random seeds above and a parameter in the search space as inputs to generate artificial statistics.

s_obs

A vector representing the observed statistic.

tol

A numeric specifying the tolerance of the confidence interval.

resolution

An integer specifying the mesh number of the search space.

theta_init

A vector specifying the starting point for the initial optim search.

T_stat

Default to the Mahalanobis distance. See Vignette for detailed explanation.

Examples

### Note that the examples may take a few seconds to run.
### Regular normal
set.seed(123)
n <- 50 # sample size
R <- 50 # Repro sample size (should be at least 200 for accuracy in practice)
alpha <- .05 # significance level
tol <- 0.01 # tolerance for the confidence set (use smaller tolerance in practice)
s_obs <- c(1.12, 0.67) # the observed sample mean
seeds <- matrix(rnorm(R * (n + 2)), nrow = R, ncol = n + 2) # pre-generated seeds

# this function computes the repro statistics given the seeds and the parameter
s_sample <- function(seeds, theta) {
  # generate the raw data points
  raw_data <- theta[1] + sqrt(theta[2]) * seeds[, 1:n]

  # compute the regular statistics
  s_mean <- apply(raw_data, 1, mean)
  s_var <- apply(raw_data, 1, var)

  return(cbind(s_mean, s_var))
}

lower_bds <- c(0.5, 0.3) # lower bounds for the parameter search region
upper_bds <- c(1.5, 1.3) # upper bounds for the parameter search region

resolution = 10  # resolution of the grid
result <- confidence_grid(alpha, lower_bds, upper_bds, seeds, s_sample, s_obs, tol, resolution)
print(result$ind_array)
print(result$search_lower_bds)
print(result$search_upper_bds)