Generate Different Types of multiplier bootstrap weights

comp_boot_mul_wgt is a Helper function for comp_boot_mul to generate different types of multiplier bootstrap weights. This section is inspired by the weighttype option in the Stata boottest package.

comp_boot_mul_wgt(n, weights_type)

Arguments

n	The number of random multiplier bootstrap weights to generate.
weights_type	The type of multiplier bootstrap weights to generate. Based on the `weighttype` option in the `Stata boottest` package, this can only take the following five pre-specified values `"rademacher", "mammen", "webb", "std_gaussian", "gamma"`. A brief description of each type is as follows. The `"rademacher"` weights are sampled from the two point Rademacher distribution which takes values \(\{1, 1\}\), with equal probability. The `"mammen"` weights are sampled from the two point Mammen distribution which has takes values \(\{\phi, 1 - \phi\}\), with probabilities \(\{\frac{\phi}{\sqrt{5}}, 1 - \frac{\phi}{\sqrt{5}}\}\), respectively. The `"webb"` weights are sampled from the six point Webb distribution which has takes values \(\{\pm \sqrt{\frac{3}{2}}, \pm \sqrt{\frac{1}{2}}, \pm 1 \}\), with equal probability. The `"std_gaussian"` weights are sampled from the standard Gaussian (normal) distribution with mean = \(0\), and variance = \(1\). Finally, the `"gamma"` weights are sampled from the Gamma distribution with shape parameter = \(4\), and scale parameter = \(1\). For more details on these weight types see see Roodman et al. (2019) .

The number of random multiplier bootstrap weights to generate.

weights_type

The type of multiplier bootstrap weights to generate. Based on the weighttype option in the Stata boottest package, this can only take the following five pre-specified values "rademacher", "mammen", "webb", "std_gaussian", "gamma". A brief description of each type is as follows. The "rademacher" weights are sampled from the two point Rademacher distribution which takes values \(\{1, 1\}\), with equal probability. The "mammen" weights are sampled from the two point Mammen distribution which has takes values \(\{\phi, 1 - \phi\}\), with probabilities \(\{\frac{\phi}{\sqrt{5}}, 1 - \frac{\phi}{\sqrt{5}}\}\), respectively. The "webb" weights are sampled from the six point Webb distribution which has takes values \(\{\pm \sqrt{\frac{3}{2}}, \pm \sqrt{\frac{1}{2}}, \pm 1 \}\), with equal probability. The "std_gaussian" weights are sampled from the standard Gaussian (normal) distribution with mean = \(0\), and variance = \(1\). Finally, the "gamma" weights are sampled from the Gamma distribution with shape parameter = \(4\), and scale parameter = \(1\). For more details on these weight types see see Roodman et al. (2019) .

Value

A numeric vector of n (sampled with replacement) random multiplier bootstrap weights based on the specified multiplier weights type.

References

Roodman D, Nielsen MØ, MacKinnon JG, Webb MD (2019). “Fast and wild: Bootstrap inference in Stata using boottest.” The Stata Journal, 19(1), 4--60.

Examples

if (FALSE) {
set.seed(824908)
# Number of multiplier weights to generate
n <- 1000

# Generate the different type of multiplier weights
rademacher_w <- comp_boot_mul_wgt(
  n = n,
  weights_type = "rademacher"
)
mammen_w <- comp_boot_mul_wgt(n = n, weights_type = "mammen")
webb_w <- comp_boot_mul_wgt(n = n, weights_type = "webb")
std_gaussian_w <- comp_boot_mul_wgt(
  n = n,
  weights_type = "std_gaussian"
)
gamma_w <- comp_boot_mul_wgt(n = n, weights_type = "gamma")
}