get_level_from_bounds_one_sided {qqconf}

Calculates Global Significance Level From Simultaneous One-Sided Bounds for Rejection Region

Description

For a one-sided test of uniformity of i.i.d. observations on the unit interval, this function will determine the significance level as a function of the rejection region. Suppose n observations are drawn i.i.d. from some CDF F(x) on the unit interval, and it is desired to test the null hypothesis that F(x) = x for all x in (0, 1) against the one-sided alternative F(x) > x. Suppose the acceptance region for the test is described by a set of lower bounds, one for each order statistic. Given the lower bounds, this function calculates the significance level of the test where the null hypothesis is rejected if at least one of the order statistics falls below its corresponding lower bound.

Usage

get_level_from_bounds_one_sided(bounds)

Arguments

bounds

Numeric vector where the ith component is the lower bound for the ith order statistic. The components must lie in [0, 1], and each component must be greater than or equal to the previous one.

Details

Uses the method of Moscovich and Nadler (2016) as implemented in Crossprob (Moscovich 2020).

Value

Global significance level

References

• Moscovich, Amit, and Boaz Nadler. "Fast calculation of boundary crossing probabilities for Poisson processes." Statistics & Probability Letters 123 (2017): 177-182.

• Amit Moscovich (2020). Fast calculation of p-values for one-sided Kolmogorov-Smirnov type statistics. arXiv:2009.04954

Examples

# For X1, X2, X3 i.i.d. unif(0, 1),
# calculate 1 - P(X(1) > .1 and X(2) > .5 and X(3) > .8),
# where X(1), X(2), and X(3) are the order statistics.
get_level_from_bounds_one_sided(bounds = c(.1, .5, .8))