Asymptotic properties of a Nadaraya-Watson type estimator for regression functions of infinite order
无限阶回归函数的 Nadaraya–Watson 型估计量及其渐近性质
We consider a class of nonparametric time series regression models in which the regressor takes values in a sequence space. Technical challenges that hampered theoretical advances in these models include the lack of associated Lebesgue density and difficulties with regard to the choice of dependence structure in the autoregressive framework. We propose an infinite-dimensional Nadaraya-Watson type estimator, and investigate its asymptotic properties in detail under both…