\(P(\|G_n - B_n(F)\|_\infty > (a\log n + x)/\sqrt n) \le
b e^{-cx}\). The universal constants a, b, c are stated NOWHERE in
the original KMT papers or in Kosorok, so they must be supplied;
Ye & Austern (2025) derive computable substitutes. Mirrors
morie.fn.ksr059.
Usage
morie_kmt_bound(n, x = 1, a = NULL, b = NULL, c = NULL)
Arguments
- n
sample size.
- x
deviation parameter.
- a, b, c
the universal constants; all three required.
Value
list: threshold, probability_bound, n.
References
Komlos, Major & Tusnady (1975), Z. Wahrsch. Verw.
Gebiete 32(1-2), 111-131. Ye, H. & Austern, M. (2025),
arXiv:2508.03833.
Examples
morie_kmt_bound(1000, x = 2, a = 1, b = 1, c = 1)$threshold
#> [1] 0.281688
