线性过程的Shannon熵估计
Shannon entropy estimation for linear processes
摘要：
本文利用概率密度函数$f(x)$估计了单边线性过程的Shannon熵$S(f) = -\E[ \log (f(x))]$.我们采用积分估计器$S_n(f)$，它利用了$f(x)$的标准核密度估计器$f_n(x)$。证明了在合理的条件下，$S_n (f)$几乎必然收敛于$S(f)$，并且收敛于$Ł^2$.
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
