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Abstract:
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Global envelope tests (Myllymäki et al. 2017, Mrkvi?ka et al. 2017) have shown good applicability in spatial statistics problems, where test statistic is usually functional. One dimensional functional statistic is usually used, but also two or three dimensional functional statistics were employed. Also combining several functional statistics in one test was applied. Recently, this theory was spread in functional linear model problems where it is used to test for significance of a factor with a graphical interpretation. The regions of significance potentially together with levels of factor are given on a global significance level. In this talk, we will show how this methodology can be used to find: 1) Joint functional box plot and joint functional clustering, which are sensitive both on magnitude outliers or differences and shape outliers or differences. 2) Independence test of two random variables which can be arbitrary, i.e. they can be continuous, categorical or combined. And further its graphical interpretation which shows the combinations of values of random variables which cause the potential dependence. 3) Graphical n-sample test of correspondence of distribution functions.
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