论文标题
线性过程的香农熵估计
Shannon entropy estimation for linear processes
论文作者
论文摘要
在本文中，我们估计了Shannon熵$ s（f）= - \ e [\ log（f（x））$的单方面线性过程，具有概率密度函数$ f（x）$。我们采用积分估算器$ s_n（f）$，它利用$ f（x）$的标准内核密度估算器$ f_n（x）$。我们表明，$ s_n（f）$几乎可以肯定地收敛到$ s（f）$，并且在合理条件下以$^2 $收敛。
In this paper, we estimate the Shannon entropy $S(f) = -\E[ \log (f(x))]$ of a one-sided linear process with probability density function $f(x)$. We employ the integral estimator $S_n(f)$, which utilizes the standard kernel density estimator $f_n(x)$ of $f(x)$. We show that $S_n (f)$ converges to $S(f)$ almost surely and in $Ł^2$ under reasonable conditions.
