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目标函数不光滑时半参数模型的估计AI 解读

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can themselves depend on the parameters to be estimated. Our results extend existing theories such as those of Pakes and Pollard (1989), Andrews (1994a), and Newey (1994). We also show that…

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多类 GARCH 与随机波动率模型的混合性和矩性质AI 解读

This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments…

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Hilbert 空间值依赖异质数组的中心极限定理与函数中心极限定理及应用AI 解读

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…

弱依赖数据下的筛极值估计AI 解读

Many non/semiparametric time series estimates may be regarded as different forms of sieve extremum estimates. For stationary absolute regular mixing observations, the authors obtain convergence rates of sieve extremurn estimates and root-n asymptotic normality of 'plug-in' sieve extremum estimates of smooth functionals. As applications to time series models, they give convergence rates for nonparametric ARX(p,q) regression via neural networks, splines, wavelets; root-n…

Hilbert 空间值 mixingale 的大数定律及其应用AI 解读

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,…