标题： 方差和偏度的有偏估计 显示英文标题

标题： Biased-estimations of the Variance and Skewness

摘要： 非线性组合的直接可观测量常用于估计理论感兴趣的量。 如果不小心，这可能导致有偏的估计。 一个非常感兴趣的例子是星系分布的偏度$S_3$，定义为三阶矩$\xibar_3$与方差平方$\xibar_2^2$的比值。 假设分别给出了$\xibar_3$和$\xibar_2^2$的无偏估计量，取两者的比值不一定导致$S_3$的无偏估计量。 正是这种估计偏差影响了大多数现有对$S_3$的测量。 此外，对于$\xibar_3$和$\xibar_2$的常见估计量也自身存在这种类型的估计偏差：对于$\xibar_2$来说，这等同于通常所知的积分约束。我们提出了一种统一的处理方法，允许所有这些估计偏差都能被解析计算。它们通常为负值，并且在给定平滑尺度下，随着调查体积的增加而显著减小。我们对一些现有的方差和偏度测量进行了重新分析，并表明，具有相似选择标准但不同大小的调查之间大多数已知的系统性差异可以归因于与体积相关的估计偏差。这会影响从这些调查中推断星系偏差。我们的方法可以适应类比量在类星体光谱和弱引力透镜图中的测量。我们提出了减少上述估计偏差的方法，并指出了其他可能遭受相同非线性估计偏差类型的LSS研究实例。 显示英文摘要

摘要： Nonlinear combinations of direct observables are often used to estimate quantities of theoretical interest. Without sufficient caution, this could lead to biased estimations. An example of great interest is the skewness $S_3$ of the galaxy distribution, defined as the ratio of the third moment $\xibar_3$ and the variance squared $\xibar_2^2$. Suppose one is given unbiased estimators for $\xibar_3$ and $\xibar_2^2$ respectively, taking a ratio of the two does not necessarily result in an unbiased estimator of $S_3$. Exactly such an estimation-bias affects most existing measurements of $S_3$. Furthermore, common estimators for $\xibar_3$ and $\xibar_2$ suffer also from this kind of estimation-bias themselves: for $\xibar_2$, it is equivalent to what is commonly known as the integral constraint. We present a unifying treatment allowing all these estimation-biases to be calculated analytically. They are in general negative, and decrease in significance as the survey volume increases, for a given smoothing scale. We present a re-analysis of some existing measurements of the variance and skewness and show that most of the well-known systematic discrepancies between surveys with similar selection criteria, but different sizes, can be attributed to the volume-dependent estimation-biases. This affects the inference of the galaxy-bias(es) from these surveys. Our methodology can be adapted to measurements of analogous quantities in quasar spectra and weak-lensing maps. We suggest methods to reduce the above estimation-biases, and point out other examples in LSS studies which might suffer from the same type of a nonlinear-estimation-bias.