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谱 Rényi 散度的稳健性AI 解读

This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $α$-Rényi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to highlight both information-theoretic and statistical properties of spectral $α$-Rényi divergences. We reveal the connection between the spectral $α$-Rényi divergence and the $γ$-divergence in robust statistics, and a variational representation of the…

一般高斯过程的最优估计AI 解读

This paper proposes a novel exact maximum likelihood (ML) estimation method for general Gaussian processes, where all parameters are estimated jointly. The exact ML estimator (MLE) is consistent and asymptotically normally distributed. We prove the local asymptotic normality (LAN) property of the sequence of statistical experiments for general Gaussian processes in the sense of Le Cam, thereby enabling optimal estimation and facilitating statistical inference. The results…

高频观测下常数漂移分数布朗运动的拟似然分析AI 解读

Consider an estimation of the Hurst parameter $H\in(0,1)$ and the volatility parameter $σ>0$ for a fractional Brownian motion with a drift term under high-frequency observations with a finite time interval. In the present paper, we propose a consistent estimator of the parameter $θ=(H,σ)$ combining the ideas of a quasi-likelihood function based on a local Gaussian approximation of a high-frequently observed time series and its frequency-domain approximation. Moreover, we…