Download Analytical Methods in Probability Theory: Proceedings of the by Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay PDF

By Harald Bergström (auth.), Daniel Dugué, Eugene Lukacs, Vijay K. Rohatgi (eds.)

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We assume that we have divided each coordinate of [0,I] p in M. subintervals, J J < ... Mp blocks, such as O = x~ < x I J = ~P x! -l''''' j 1 i j p -I ,... 'X pi -I ). + (-I) p W (x I p Likewise, define Xn;il Xn;il,''',i p . ,Ip . ~ip 2 Let also i dDl(~)). ,i p B. ,i p Consider a set of independent Gaussian centered random variables indexed on the same set of blocks : Zil .... % N(O, SB dDl(~) ) % N(O,o~ ,ip). ':p . ,i p Lemma 9 . The joint distribution of {X ,i . } is the same as the joint dis~" ] , .

Under dependence function dependence function its standard version. - u Lemma 7 . - u Lemma 8 . -~ i , ~] x squares mass under p=2. [ -' ~ in the ~ , n a different of multivariate Take a square J , ~1 ... = C j grid. - a sufficient on X l , . . , X n- studied among of view. of dependence functions, t o be q u i t e usefull which in appre- samples. Darken then squares, rank of the function statistics [0,1] 2 divided c a n be s e e n on I ~ ) of rank statistics point visualisation 1 / n on e a c h o f t h e s e measure up t o an e q u i v a l e n c e to multivariate and w h i c h h a s p r o v e d structure assume that set non parametric reIated [ 12], by t h e the empirical free a statistical we h a v e named d e p e n d o g r a m , ciating that closely (defined , up t o a n a r b i t r a r y distribution (3) function defined 1 ~ j ~ p} lemma i m p l i e s for Note that others dependence that the if resulting in n 2 identical C rk(1),rk(2), one puts measure sub- to obtain an u n i f o r m is the mea- standard n 45 Now take an arbitrary p.

274-292. , Acad. Press. , Springer Verlag lecture notes. [ 5] 1981, A Kolmogorov-Smirnov test for independence, accepted for publication in Revue Roum. Math. Pures Appl. [ 6] 1981, Some applications of the dependence tistical inference, Coll. Math. , North Holland. [ 7] 1981, An asymptotic decomposition independence, Accepted for publication for multivariate tests of in the Journal of Multivariate Analysis. , 1977, The analysis of contingency tables, Chapman & Hall. , 1951, Sur les tableaux de correlation dont les marges sont donn~es, Ann.

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