Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes
Sen, Pranab Kumar
Ann. Probab., Tome 2 (1974) no. 6, p. 147-154 / Harvested from Project Euclid
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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.
Publié le : 1974-02-14
Classification:  $D^p \lbrack 0, 1 \rbrack$ space,  empirical processes,  Gaussian process,  random sample size,  Skorokhod $J_1$-topology,  tightness,  weak convergence,  60F05,  60B10 
@article{1176996760,
     author = {Sen, Pranab Kumar},
     title = {Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes},
     journal = {Ann. Probab.},
     volume = {2},
     number = {6},
     year = {1974},
     pages = { 147-154},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176996760}
}

Sen, Pranab Kumar. Weak Convergence of Multidimensional Empirical Processes for Stationary $\phi$-Mixing Processes. Ann. Probab., Tome 2 (1974) no. 6, pp.  147-154. http://gdmltest.u-ga.fr/item/1176996760/