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• W1576591627 abstract "We obtain new CLTs and FCLTs for Hilbert-valued arrays near epoch dependent on mixing processes, as well as new FCLTs for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent observations: (1) A new CLT for any plug-in estimator of a cumulative distribution function (e.g., an empirical cdf, or a cdf estimator based on a kernel density estimator), which can in turn deliver distribution results for many Von Mises functionals; (2) A new limiting distribution result for degenerate U-statistics, which delivers distribution results for Bierens' integrated conditional moment tests; (3) A new functional central limit result for Hilbert-valued stochastic approximation procedures, which delivers distribution results for nonparametric recursive generalized method of moment estimators, including nonparametric adaptive learning models." @default.
• W1576591627 created "2016-06-24" @default.
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• W1576591627 date "1998-01-01" @default.
• W1576591627 modified "2023-09-23" @default.
• W1576591627 title "Central Limit and Functional Central Limit Theorems for Hilbert-Valued Dependent Heterogeneous Arrays with Applications" @default.
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• W1576591627 doi "https://doi.org/10.2139/ssrn.51140" @default.
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