Electronic Journal of Probability

Weak Convergence for the Row Sums of a Triangular Array of Empirical Processes Indexed by a Manageable Triangular Array of Functions

Miguel Arcones

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We study the weak convergence for the row sums of a general triangular array of empirical processes indexed by a manageable class of functions converging to an arbitrary limit. As particular cases, we consider random series processes and normalized sums of i.i.d. random processes with Gaussian and stable limits. An application to linear regression is presented. In this application, the limit of the row sum of a triangular array of empirical process is the mixture of a Gaussian process with a random series process.

Article information

Electron. J. Probab., Volume 4 (1999), paper no. 7, 17 pp.

Accepted: 23 April 1999
First available in Project Euclid: 4 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 60F15: Strong theorems

Empirical processes triangular arrays manageable classes

This work is licensed under aCreative Commons Attribution 3.0 License.


Arcones, Miguel. Weak Convergence for the Row Sums of a Triangular Array of Empirical Processes Indexed by a Manageable Triangular Array of Functions. Electron. J. Probab. 4 (1999), paper no. 7, 17 pp. doi:10.1214/EJP.v4-44. https://projecteuclid.org/euclid.ejp/1457125516

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