Nonparametric Analysis of Bivariate Censored Data.

Cover Nonparametric Analysis of Bivariate Censored Data.
Nonparametric Analysis of Bivariate Censored Data.
Popovich, Edward Anthony, 1957-
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^ (b) ^ L SI with probability one, (c) There exists a constant L such that p-lim L = L as n-*".
The proposed test statistic is T^(N^,N2) = (1-L^^)^ T^*(N^) . L^^ T^^^) .
* Note that under H and conditional on N.=n,, i=l,2, T. (N ) has a o XI In 1 distribution which is the same as the distribution of a standardized Wilcoxon signed rank statistic based on n observations (Randies and Wolfe, 1979), while T. (N.) is distributed as an independent -29- standardlzed Binomial random variable with parame
...ters n. and J5.
Therefore, T (N, ,N_) is conditionally distribution-free under H and a n 1 Z o test of H can be based on T (N,,N-), o n i / Hereafter, for the sake of simplicity T (n.,n2) will denote the statistic T (N, ,N-) conditioned on N,=n. , i=l,2 . Useful n i z 11 properties of T (n. ,n_) are stated in Lemma 3.2.1.
Lemma 3.2.1: Under H : 9=0 and (Al) , (A2) , (A3), and (A5) , — — — — — o (a) Eq [T^(n^,n2)] = 0, (b) Varp [T^(nj,n2)] = 1, (c) T (n,,n-) is symmetrically distributed about 0.


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