Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications

Xiaohong Chen and Halbert White

Econometric Theory, 1996, vol. 12, issue 02, pages 284-304

Abstract: To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valued Lp mixingales 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 Theory 4, 458 221; 1992, Econometric Theory 8, 421 304), and de Jong (1995, Econometric Theory 11, 347 358), extending results for H = R and improving memory conditions in certain instances. We give as examples consistency results for series and kernel estimators.

Date: 1996

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Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:12:y:1996:i:02:p:284-304_00

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