| boot.pval {boot.pval} | R Documentation |
Compute Bootstrap p-values
Description
Compute bootstrap p-values through confidence interval inversion, as described in Hall (1992) and Thulin (2021).
Usage
boot.pval(boot_res, type = "perc", theta_null = 0, pval_precision = NULL, ...)
Arguments
boot_res |
An object of class "boot" containing the output of a bootstrap calculation. |
type |
A vector of character strings representing the type of interval to base the test on. The value should be one of "norm", "basic", "stud", "perc" (the default), and "bca". |
theta_null |
The value of the parameter under the null hypothesis. |
pval_precision |
The desired precision for the p-value. The default is 1/R, where R is the number of bootstrap samples in |
... |
Additional arguments passed to |
Details
p-values can be computed by inverting the corresponding confidence intervals, as described in Section 12.2 of Thulin (2021) and Section 3.12 in Hall (1992). This function computes p-values in this way from "boot" objects. The approach relies on the fact that:
the p-value of the two-sided test for the parameter theta is the smallest alpha such that theta is not contained in the corresponding 1-alpha confidence interval,
for a test of the parameter theta with significance level alpha, the set of values of theta that aren't rejected by the two-sided test (when used as the null hypothesis) is a 1-alpha confidence interval for theta.
Value
A bootstrap p-value.
References
Hall P (1992). The Bootstrap and Edgeworth Expansion. Springer, New York. ISBN 9781461243847.
Thulin M (2021). Modern Statistics with R. Eos Chasma Press, Uppsala. ISBN 9789152701515, https://www.modernstatisticswithr.com/.
Examples
# Hypothesis test for the city data
# H0: ratio = 1.4
library(boot)
ratio <- function(d, w) sum(d$x * w)/sum(d$u * w)
city.boot <- boot(city, ratio, R = 99, stype = "w", sim = "ordinary")
boot.pval(city.boot, theta_null = 1.4)
# Studentized test for the two sample difference of means problem
# using the final two series of the gravity data.
diff.means <- function(d, f)
{
n <- nrow(d)
gp1 <- 1:table(as.numeric(d$series))[1]
m1 <- sum(d[gp1,1] * f[gp1])/sum(f[gp1])
m2 <- sum(d[-gp1,1] * f[-gp1])/sum(f[-gp1])
ss1 <- sum(d[gp1,1]^2 * f[gp1]) - (m1 * m1 * sum(f[gp1]))
ss2 <- sum(d[-gp1,1]^2 * f[-gp1]) - (m2 * m2 * sum(f[-gp1]))
c(m1 - m2, (ss1 + ss2)/(sum(f) - 2))
}
grav1 <- gravity[as.numeric(gravity[,2]) >= 7, ]
grav1.boot <- boot(grav1, diff.means, R = 99, stype = "f",
strata = grav1[ ,2])
boot.pval(grav1.boot, type = "stud", theta_null = 0)