[Authors] Norbert Henze, Ya. Yu. Nikitin, Bruno Ebner [Title] Integral distribution-free statistics of $L_p$-type and their asymptotic comparison [AMS Subj-class] 62G10 Hypotheses testing 60F25 $L^p$-limit theorems [Keywords] empirical process, omega-square statistic, Kolmogorov-Smirnov statistic, approximate Bahadur efficiency, shift alternatives, scale alternatives, skew alternatives, test for independence, goodness-of-fit test [Abstract] Generalizing the Cram\'er-von Mises and the Kolmogorov-Smirnov test, different integral statistics based on $L_p$-norms are compared with respect to local approximate Bahadur efficiency. Simulation results corroborate the theoretical findings. Several examples illustrate that goodness-of-fit testing based on $L_p$-norms should receive more attention. It is shown that, given a distribution function $F_0$ and a specific alternative, one can draw the plot of efficiency as a function of $p$ and determine the value of $p$ giving the maximum efficiency. [Comments] English, 22 pp. The paper is accepted by the journal Computational Statistics and Data Analysis (Elsevier). [Contact e-mail] yanikit47@mail.ru