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**Additional info for Absolutely summing operators from the disc algebra**

**Sample text**

We consider all test statistics except Lo and U r as these tests are only useful to detect a downward trend. As we have in both time series monthly observations for more than 115 years, we choose the splitting factor k as multiples of 12, more precisely k ∈ {12, 24, 60, 120, 240, 360}. This guarantees that even R3 , R4 (with γ = 13 ) and N3 (with ν j = 13 n j ) can be computed for each split. For every test procedure we use the asymptotic critical values, which seems to be reasonable for the above k.

05, this test was discarded. From now on we will also refer to all introduced tests by using the names of their corresponding test statistics. 1 Layout of the simulation study A simulation study was carried out to investigate the power of the five presented tests (namely the LRT , LRM, GMT , GMM, and MDT ) over the alternative space and to compare the maximum tests with their sum based counterparts. Only data with a positive trend in the survival functions, as imposed by the alternative in (1), was simulated.

Here interest may focus on detecting dose dependent trends in the underlying survival functions of the groups. So if a test is to be applied we are faced with an ordered alternative in the test problem, and therefore a trend test may be preferable. , the logrank test for trend, the one by Gehan [4] and Mantel [12], the one by Magel and Degges [11], and the modified ordered logrank test by Liu et al. [10], where the latter is shown to be a special case of the logrank test for trend. Due to their similarity to single contrast tests it is suspected that these tests are more powerful for certain trends than for others.

### Absolutely summing operators from the disc algebra

by Thomas

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