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1999 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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Electron. J. Probab. 4: 1-17 (1999). DOI: 10.1214/EJP.v4-44

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.

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Miguel Arcones. "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 1 - 17, 1999. https://doi.org/10.1214/EJP.v4-44

Information

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

zbMATH: 0936.60036
MathSciNet: MR1684153
Digital Object Identifier: 10.1214/EJP.v4-44

Subjects:
Primary: 60B12
Secondary: 60F15

Keywords: Empirical processes , manageable classes , triangular arrays

Vol.4 • 1999
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