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依赖数据密度估计中的带宽选择AI 解读

We address the empirical bandwidth choice problem in cases where the range of dependence may be virtually arbitrarily long. Assuming that the observed data derive from an unknown function of a Gaussian process, it is argued that, unlike more traditional contexts of statistical inference, in density estimation there is no clear role for the classical distinction between short- and long-range dependence. Indeed, the "boundaries" that separate different modes of behaviour for…

时间序列中的非参数函数估计AI 解读

Consider a stationary time series $(\mathbf{X}_t, Y_t), t = 0, \pm 1,\ldots,$ with $\mathbf{X}_t$ being $\mathbb{R}^d$-valued and $Y_t$ real-valued. The conditional mean function is given by $\theta(\mathbf{X}_0) = E(Y_0\mid\mathbf{X}_0)$. Under appropriate regularity conditions, a local average estimator of this function based on a finite realization $(\mathbf{X}_1, Y_1),\ldots,(\mathbf{X}_n, Y_n)$ can be chosen to achieve the optimal rate of convergence $n^{-1/(2 + d)}$ bot…