Laws of Large Numbers for Hilbert Space-Valued Mixingales with Applications
引入希尔伯特空间值的Lp混合序列和近邻依赖数组概念，利用新的指数不等式证明弱大数定律和强大数定律，并给出级数估计量和核估计量的一致性的例子，适用于计量经济学中的非参数估计。
To obtain consistency results for nonparametric estimators based on stochastic processes relevant in econometrics, we introduce the notions of Hilbert space-valued L p 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, 458–467), Hansen (1991, Econometric Theory 7, 213–221; 1992, Econometric Theory 8, 421–422), Davidson (1993, Statistics and Probability Letters 16,301–304), 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.