Author:
Chen Xiaohong,White Halbert
Abstract
To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valuedLpmixingales and near-epoch dependent arrays, and we prove weak and strong laws of large numbers by using a new exponential inequality for Hilbert (H) space-valued martingale difference arrays. We follow Andrews (1988,Econometric Theory4, 458–467), Hansen (1991,Econometric Theory7, 213–221; 1992,Econometric Theory8, 421–422), Davidson (1993,Statistics and Probability Letters16,301–304), and de Jong (1995,Econometric Theory11, 347–358), extending results forH= R and improving memory conditions in certain instances. We give as examples consistency results for series and kernel estimators.
Publisher
Cambridge University Press (CUP)
Subject
Economics and Econometrics,Social Sciences (miscellaneous)
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4. Chen X. & White H. (1992c). Asymptotic Properties of Some Projection-Based Robbins-Monro Procedures in a Hilbert Space. Discussion paper 92-46, UCSD Department of Economics.
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