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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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1457125516

Digital Object Identifier
doi:10.1214/EJP.v4-44

Mathematical Reviews number (MathSciNet)
MR1684153

Zentralblatt MATH identifier
0936.60036

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

Keywords
Empirical processes triangular arrays manageable classes

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

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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