The Annals of Statistics

The Asymptotic Distribution Theory of the Empiric CDF for Mixing Stochastic Processes

Joseph L. Gastwirth and Herman Rubin

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Abstract

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.

Article information

Source
Ann. Statist., Volume 3, Number 4 (1975), 809-824.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343184

Digital Object Identifier
doi:10.1214/aos/1176343184

Mathematical Reviews number (MathSciNet)
MR385952

Zentralblatt MATH identifier
0318.62016

JSTOR
links.jstor.org

Subjects
Primary: 62E20: Asymptotic distribution theory
Secondary: 60F05: Central limit and other weak theorems 60G10: Stationary processes

Keywords
Asymptotic distribution empiric distribution function strong mixing stationary processes

Citation

Gastwirth, Joseph L.; Rubin, Herman. The Asymptotic Distribution Theory of the Empiric CDF for Mixing Stochastic Processes. Ann. Statist. 3 (1975), no. 4, 809--824. doi:10.1214/aos/1176343184. https://projecteuclid.org/euclid.aos/1176343184


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