Asymptotic Confidence Intervals for the Mean with Increased Finite-Sample Coverage Probabilities

We consider a Student process based on independent copies of a random variable X. If X is in the domain of attraction of the normal law (DAN), a weighted version of the Student process is known to follow a functional Central Limit Theorem (FCLT). Accordingly, appropriate functionals of such a process converge in distribution to the same functionals of the similarly weighted standard Wiener process. We use such a convergence for an integral functional and derive asymptotic confidence intervals (CIs) for the mean of X. For right-skewed distributions of X in DAN, we show that the obtained CIs have higher finite-sample coverage probabilities than, and may be preferred over, a CI I1 of the same asymptotic confidence level 1−α that is based on the CLT for the Student t-statistic, since the finite-sample coverage probabilities of the latter CI may be lower than 1−α. Moreover, for such distributions, the finite-sample coverage probabilities of our best two CIs are also higher than those of their respective equal-expected-length I1 counterparts.