This paper introduces a new mixing condition for stationary processes which is weaker than $\phi$-mixing but stronger than strong mixing. Many processes arising in applications, e.g., first order autoregressive processes, obey the conditions. The main result is that the empiric cdf of a sample from such processes converges to a Gaussian process.
Publié le : 1975-07-14
Classification:
Asymptotic distribution,
empiric distribution function,
strong mixing,
stationary processes,
62E20,
60F05,
60G10
@article{1176343184,
author = {Gastwirth, Joseph L. and Rubin, Herman},
title = {The Asymptotic Distribution Theory of the Empiric CDF for Mixing Stochastic Processes},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 809-824},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343184}
}
Gastwirth, Joseph L.; Rubin, Herman. The Asymptotic Distribution Theory of the Empiric CDF for Mixing Stochastic Processes. Ann. Statist., Tome 3 (1975) no. 1, pp. 809-824. http://gdmltest.u-ga.fr/item/1176343184/