The Annals of Statistics

Convergence of the Reduced Empirical Process for Non-I.I.D. Random Vectors

Georg Neuhaus

Full-text: Open access

Abstract

Any triangular array of row independent random vectors with continuous df's has a standard reduction to random vectors with values in the unit cube. The reduced empirical process belonging to the transformed random vectors is always relatively compact. Weak convergence to a (necessarily Gaussian) process holds iff the corresponding covariance kernel converges pointwise.

Article information

Source
Ann. Statist., Volume 3, Number 2 (1975), 528-531.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176343084

Digital Object Identifier
doi:10.1214/aos/1176343084

Mathematical Reviews number (MathSciNet)
MR380917

Zentralblatt MATH identifier
0303.62014

JSTOR
links.jstor.org

Subjects
Primary: 60B10: Convergence of probability measures
Secondary: 60G15: Gaussian processes

Keywords
Non. i.i.d. random-vectors convergence of the empirical process

Citation

Neuhaus, Georg. Convergence of the Reduced Empirical Process for Non-I.I.D. Random Vectors. Ann. Statist. 3 (1975), no. 2, 528--531. doi:10.1214/aos/1176343084. https://projecteuclid.org/euclid.aos/1176343084


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