| 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 \({I_0}\). |
