The paper supplies computable KMT-type bounds for bounded i.i.d. sums that depend only on range and variance (or an empirical estimate), plus a moderate-deviation byproduct.
Probability bounds for first exits through moving boundaries
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Computable Bounds for Strong Approximations with Applications
The paper supplies computable KMT-type bounds for bounded i.i.d. sums that depend only on range and variance (or an empirical estimate), plus a moderate-deviation byproduct.