论文标题
长记忆线性过程的内核熵估计无限差异
Kernel entropy estimation for long memory linear processes with infinite variance
论文作者
论文摘要
令$ x = \ {x_n：n \ in \ mathbb {n} \} $是一个长的内存线性过程，在吸引$α$稳定的法律$（0 <α<2）$的领域中具有创新。假设线性过程$ x $具有有界的概率密度函数$ f（x）$。 Then, under certain conditions, we consider the estimation of the quadratic functional $\int_{\mathbb{R}} f^2(x) \,dx$ by using the kernel estimator \[ T_n(h_n)=\frac{2}{n(n-1)h_n}\sum_{1\leq j<i\leq n} k \ left（\ frac {x_i-x_j} {h_n} \ right）。 \]还给出了具有对称$α$稳定创新的长记忆线性过程的仿真研究。
Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process with innovations in the domain of attraction of an $α$-stable law $(0<α<2)$. Assume that the linear process $X$ has a bounded probability density function $f(x)$. Then, under certain conditions, we consider the estimation of the quadratic functional $\int_{\mathbb{R}} f^2(x) \,dx$ by using the kernel estimator \[ T_n(h_n)=\frac{2}{n(n-1)h_n}\sum_{1\leq j<i\leq n}K\left(\frac{X_i-X_j}{h_n}\right). \] The simulation study for long memory linear processes with symmetric $α$-stable innovations is also given.
