jaroslav hajek and asymptotic theory of rank tests - Kybernetika
jaroslav hajek and asymptotic theory of rank tests - Kybernetika
jaroslav hajek and asymptotic theory of rank tests - Kybernetika
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Jaroslav Hajek <strong>and</strong> Asymptotic Theory <strong>of</strong> Rank Tests 241<br />
Theorem 2.2. (Asymptotic representation) Under (l)-(3) <strong>and</strong> (5),<br />
where<br />
[Nu] denotes the integer part <strong>of</strong> Nu <strong>and</strong><br />
S N = T N + r N , (9)<br />
At<br />
T N = Y^c Ni a N ([NUi] + l), (10)<br />
i_l<br />
Er N /var T N -> 0 as N -> oo. (11)<br />
Among various possible choices <strong>of</strong> the a Ni , Hajek also considered<br />
a Ni = E((p(U!)\R N i = i) = E
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