Abstract
For a stationary $\phi$-mixing sequence of stochastic $p(\geqq 1)$-vectors, weak convergence of the empirical process (in the $J_1$-topology on $D^p\lbrack 0, 1 \rbrack)$ to an appropriate Gaussian process is established under a simple condition on the mixing constants $\{\phi_n\}$. Weak convergence for random number of stochastic vectors is also studied. Tail probability inequalities for Kolmogorov Smirnov statistics are provided.
Citation
Pranab Kumar Sen. "Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes." Ann. Probab. 2 (1) 147 - 154, February, 1974. https://doi.org/10.1214/aop/1176996760
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