Kernel entropy estimation for linear processes II

Let $X=\{X_n:n\in \mathbb{N}\}$ be a linear process with bounded probability density function $f(x)$. Under certain conditions, we use the kernel estimator $$\frac{2}{n(n-1)h_n}\sum _{1\le i<j\le n}K\left(\frac{X_i-X_j}{h_n}\right)$$ to estimate the quadratic functional of ${\int }_{\mathbb{R}}{f}^2(x)dx$ of the linear process $X=\{X_n:n\in \mathbb{N}\}$ and improve the corresponding results in [4].