Weak Convergence for the Row Sums of a Triangular Array of Empirical Processes Indexed by a Manageable Triangular Array of Functions
Miguel A. Arcones, State University of New York
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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