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 $$\frac{2}{n(n-1)h_n} \sum_{1\le i<j\le n}K\Big(\frac{X_i-X_j}{h_n}\Big)$$ 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].