Sequential two-fold Pearson chi-squared test and tails of the Bessel process distributions

TL;DR

This paper derives asymptotic error probability formulas for a two-fold Pearson goodness-of-fit test, linking them to the tail behavior of Bessel process distributions and exploring properties of the Infeld function.

Contribution

It introduces new asymptotic formulas for error probabilities of a two-fold Pearson test and connects these to the tails of Bessel process distributions, including properties of the Infeld function.

Findings

Asymptotic formulas for error probabilities are established.

Results relate test error probabilities to Bessel process tail distributions.

Properties of the Infeld function are characterized.

Abstract

We find asymptotic formulas for error probabilities of two-fold Pearson goodness-of-fit test as functions of two critical levels. These results may be reformulated in terms of tails of two-dimensional distributions of the Bessel process. Necessary properties of the Infeld function are obtained.