标题： 非高斯卡方方法与多变量埃奇沃思展开 显示英文标题

标题： Non-Gaussian Chi-squared method with the multivariate Edgeworth expansion

摘要： 我在这里提出了最大似然方法和$\chi^2$方法的推广，适用于数据被假设为{\it 不是}高斯分布的情况。 该方法基于多元Edgeworth展开，可以找到多个天体物理学应用。 我仅提及其中两个。 首先，在微波背景分析中，不能排除初始扰动是非高斯的。 其次，在大尺度结构统计中，因为我们已经知道在非线性重要的尺度上，星系分布偏离高斯性。 作为第一个有趣的结果，我在这里展示了当考虑非高斯性时置信区域是如何改变的。 显示英文摘要

摘要： I present here a generalization of the maximum likelihood method and the $\chi^2$ method to the cases in which the data are {\it not} assumed to be Gaussian distributed. The method, based on the multivariate Edgeworth expansion, can find several astrophysical applications. I mention only two of them. First, in the microwave background analysis, where it cannot be excluded that the initial perturbations are non-Gaussian. Second, in the large scale structure statistics, as we already know that the galaxy distribution deviates from Gaussianity on the scales at which non-linearity is important. As a first interesting result I show here how the confidence regions are modified when non-Gaussianity is taken into account.