| Abstract: | We take a Student process that is based on independent copies of a random variable ({X}) and has trajectories in the function space ({D})[0, 1]. As a consequence of a functional central limit theorem (FCLT) for this process, with ({X}) in the domain of attraction of the normal law, we consider convergence in distribution of five functionals of this process and derive respective asymptotic confidence intervals for the mean of ({X}). We conclude that the obtained intervals have higher finite-sample coverage probabilities, or shorter expected lengths, than those of a classical asymptotic confidence interval, ({I_0}), that follows simply from the asymptotic normality of the Student ({t})-statistic. Thus, the five FCLT based intervals may present reasonable alternatives to ({I_0}). |
