Limit Theorems for Empirical Processes Based on Dependent Data

Patrizia Berti, Luca Pratelli and Pietro Rigo
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Patrizia Berti: Department of Mathematics, University of Modena and Reggio Emilia
Luca Pratelli: Accademia Navale di Livorno
Pietro Rigo: Department of Economics and Quantitative Methods, University of Pavia

No 132, Quaderni di Dipartimento from University of Pavia, Department of Economics and Quantitative Methods

Abstract: Empirical processes for non ergodic data are investigated under uniform distance. Some CLTs, both uniform and non uniform, are proved. In particular, conditions for Bn = n^(1/2) (µn - bn) and Cn = n^(1/2) (µn - an) to converge in distribution are given, where µn is the empirical measure, an the predictive measure, and bn = 1/n sum (ai) for i=0 to n-1. Such conditions can be applied to any adapted sequence of random variables. Various examples and a characterization of conditionally identically distributed sequences are given as well.

Keywords: Conditional identity in distribution; empirical process; exchangeability; predictive measure; stable convergence. (search for similar items in EconPapers)
Pages: 16 pages
Date: 2010-11
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