This paper gives simple nonuniform bounds on the tail areas of the permutation distribution of the usual Student's <italic>t</italic>-statistic when the observations are independent with symmetric distributions. As opposed to uniform bounds, nonuniform bounds depend on the observed sample. It is shown that the...

Locally asymptotically optimal tests are derived for the null hypothesis of traditional AR dependence, with unspecified AR coefficients and unspecified innovation densities, against an alternative of periodically correlated AR dependence. Parametric and nonparametric rank-based versions are...

A Sharpening Of Nonuniform bounds of the Berry-Esseen type initially obtained by Esseen and later generalized by Kolodjažnyĭ–who also proved that they are, in some sense, optimal–is proposed. Further, the corresponding inequalities are shown to provide uniformly improved Chebyshev bounds...