A new modification of the minimum-contrast estimator (the weighted MCE) of drift parameter in a linear stochastic evolution equation with additive fractional noise is introduced in the setting of the spectral approach (Fourier coordinates of the solution are observed). The reweighing technique, which utilizes the self-similarity property, achieves strong consistency and asymptotic normality of the estimator as number of coordinates increases and time horizon is fixed (the space consistency). In this respect, this modification outperforms the standard (non-weighted) MCE. Compared to other drift estimators studied within spectral approach (e.g., maximum likelihood, trajectory fitting), the weighted MCE is rather universal. It covers discrete time as well as continuous-time observations and it is applicable to processes with any value of Hurst index [Formula: see text]. To the author’s best knowledge, this is so far the first space-consistent estimator studied for [Formula: see text].

中文翻译：

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线性随机演化方程的最小对比度估计量的空间一致版本

在光谱方法的设置中引入了对具有加性分数噪声的线性随机演化方程中漂移参数的最小对比度估计量（加权MCE）的新修改（观察解的傅立叶坐标）。利用自相似性的重新加权技术，随着坐标数量的增加和时间范围的固定（空间一致性），实现了估计量的强一致性和渐近正态性。在这方面，这种修改优于标准（非加权）MCE。与在谱方法中研究的其他漂移估计量（例如，最大似然、轨迹拟合）相比，加权 MCE 相当普遍。它涵盖离散时间和连续时间观察，适用于任何赫斯特指数值的过程[公式：见正文]。据作者所知，这是迄今为止为 [公式：见正文] 研究的第一个空间一致估计器。