Edge case were the confidence interval converges to theta_null

[mthulin]

Issue submitted via e-mail:

I may have found an edge case for which p-values inconsistent with the confidence interval are returned. Here is a minimal reproducible example along with a guess as to what the cause is.

test_df <- data.frame("x" = c(rep(-1, 3),
rep(0, 14),
rep(1, 3)))
statistic <- function(data, indices) mean(data$x[indices])

set.seed(24601)
boot_res <- boot(test_df, statistic, 1000)

table(boot_res$t)

-0.4 -0.35 -0.3 -0.25 -0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

1 5 5 19 46 66 109 166 169 155 96 78 60

0.25 0.3 0.35 0.5

16 6 2 1

boot.ci(boot_res, type = "perc")

BOOTSTRAP CONFIDENCE INTERVAL CALCULATIONS

Based on 1000 bootstrap replicates

CALL :

boot.ci(boot.out = boot_res, type = "perc")

Intervals :

Level Percentile

95% (-0.2500, 0.2487 )

Calculations and Intervals on Original Scale

boot.pval(boot_res, type = "perc")

[1] 0.001

The confidence interval contains zero, but the p-value comes back as highly significant.

pval_precision <- NULL
type <- "perc"
theta_null <- 0

if (is.null(pval_precision)) {
pval_precision = 1 / boot_res$R
}
alpha_seq <- seq(1e-16, 1 - 1e-16, pval_precision)
ci <- boot::boot.ci(boot_res,
conf = 1 - alpha_seq, type = type)

Warning in norm.inter(t, alpha): extreme order statistics used as endpoints

bounds <-
switch(
type,
norm = ci$normal[, 2:3],
basic = ci$basic[,
4:5],
stud = ci$student[, 4:5],
perc = ci$percent[, 4:5],
bca = ci$bca[, 4:5]
)
alpha <- alpha_seq[which.min(theta_null >= bounds[, 1] &
theta_null <= bounds[, 2])]
The problem is which.min(theta_null >= bounds[, 1] & theta_null <= bounds[, 2]). I believe the intention is to find the first FALSE value, but in this case there are no false values, and it’s picking up the first non-NA value in alpha_seq and falsely communicating high significance.