A common way to calculate the glitch activity of a pulsar is an ordinary linear regression of the observed cumulative glitch history. This method however is likely to underestimate the errors on the activity, as it implicitly assumes a (long-term) linear dependence between glitch sizes and waiting times, as well as equal variance, i.e., homoscedasticity, in the fit residuals, both assumptions that are not well justified from pulsar data. In this paper, we review the extrapolation of the glitch activity parameter and explore two alternatives: the relaxation of the homoscedasticity hypothesis in the linear fit and the use of the bootstrap technique. We find a larger uncertainty in the activity with respect to that obtained by ordinary linear regression, especially for those objects in which it can be significantly affected by a single glitch. We discuss how this affects the theoretical upper bound on the moment of inertia associated with the region of a neutron star containing the superfluid reservoir of angular momentum released in a stationary sequence of glitches. We find that this upper bound is less tight if one considers the uncertainty on the activity estimated with the bootstrap method and allows for models in which the superfluid reservoir is entirely in the crust.

中文翻译：

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脉冲星小故障活动的统计估计

计算脉冲星的毛刺活动的一种常用方法是观察到的累积毛刺历史的普通线性回归。但是，该方法可能低估了活动的误差，因为它隐含地假设了故障大小和等待时间之间的（长期）线性相关性，以及拟合残差中的均方差（即均方差），这两个假设都表明脉冲星数据并不能很好地证明这一点。在本文中，我们回顾了毛刺活动性参数的外推法，并探讨了两种选择：线性拟合中的均方差假设的松弛和自举技术的使用。我们发现，与通过普通线性回归获得的活动相比，活动的不确定性更大，尤其是对于那些可能受到单个故障显着影响的对象。我们讨论了这如何影响与包含在固定故障序列中释放的角动量的超流体储层的中子星区域相关的惯性矩的理论上限。我们发现，如果考虑自举法估计的活动的不确定性，并允许超级流体储层完全位于地壳中的模型，则该上限不太紧。