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

Miguel Arcones
1999 Electronic Journal of Probability  
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
more » ... n process with a random series process.
doi:10.1214/ejp.v4-44 fatcat:hiv2khlgzfbpbosvhq2ictvnba