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This effectively associates random data with each gene's neighborhood.
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Meanwhile, the nonparametric estimation and nonparametric tests for association and negatively associated random variables can be found in Prakasa Rao [25].
In particular, the classical Marcinkiewicz strong law of large numbers for negatively associated random variables is generalized to the case of asymptotically negative association.
Let be a sequence of negatively associated random variables.
Note that for For each fixed are bounded by If are negatively associated random variables, then are also negatively associated random variables, since are monotone transformations of.
Our results partially extend the corresponding ones for independent random variables and negatively associated random variables.
Results are obtained for negatively associated random fields and ρ ∗ -mixing random fields.
Sharp convergence rates for fixed design regression estimators for negatively associated random variables are established.
Chen et al. [9] extended Theorem 1.2 to negatively associated random variables.
Since are also negatively associated random variables, we can replace by in the above statement.
Hence Corollaries 3.3 3.6 hold for arrays of rowwise negatively associated random variables.
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