On application of the \(\omega^2\) goodness-of-fit test for testing the hypothesis that the observed random vector is from a parametric set (Q2739832)

The \(\omega^2\) goodness-of-fit test is considered for vector-valued observations. Upper bounds for the probability of the first type error are obtained for simple null hypotheses and for the case when the parameters are estimated by the ``minimum of \(\omega^2\)'' method.NEWLINENEWLINENEWLINENote, that the bounds in the paper are derived only asymptotically (as the sample size tends to infinity). The proof seems dubious since at the step when the problem is reduced to the testing for \([0,1]^n\)-uniform distributions, the author simply uses marginal quantile transforms and refers to analogous one-dimensional procedures avoiding the problem of dependent components.