On the corporate of the coverage probability of a sequential confidence interval based on the sign test

Abstract

The convergence rate of the remainder term of the coverage probability of a sequential confidence interval based on the sign test is studied as the prescribed length of the interval tends to zero. Since the coverage probability can be expressed in terms of partial sums of symmetric Bernoulli random variables, it is possible to use and adapt a Berry–Esseen type theorem for a stochastic number of summands in order to obtain an explicit asymptotic bound for the remainder term.

Keywords:

• Order statistics
• remainder term
• Berry–Esseen theorm
• Bernoulli random variables
• asymptotic distribution