CENTRAL LIMIT AND FUNCTIONAL CENTRAL LIMIT THEOREMS FOR HILBERT-VALUED DEPENDENT HETEROGENEOUS ARRAYS WITH APPLICATIONS
为希尔伯特空间值相依异质数组建立了新的中心极限定理和泛函中心极限定理，可用于推导时间序列计量经济学中参数和非参数估计量的渐近分布，并给出了三个重要应用。
We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's 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 (c.d.f.) (e.g., an empirical c.d.f., or a c.d.f. 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's 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.