Asymptotic Normality of the Recursive Kernel Regression Estimate Under Dependence Conditions
依赖条件下递归核回归估计的渐近正态性
For $i = 1,2,\ldots$, let $X_i$ and $Y_i$ be $\mathbb{R}^d$-valued ($d \geq 1$ integer) and $\mathbb{R}$-valued, respectively, random variables, and let $\{(X_i, Y_i)\}, i \geq 1$, be a strictly stationary and $\alpha$-mixing stochastic process. Set $m(x) = \mathscr{E}(Y_1\mid X_1 = x), x \in \mathbb{R}^d$, and let $\hat{m}_n(x)$ be a certain recursive kernel estimate of $m(x)$. Under suitable regularity conditions and as $n \rightarrow \infty$, it is shown that $\hat{m}_n(x)$…