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地球物理张量特征值的非参数自助法推断AI 解读

Symmetric matrices (tensors) are measured in geophysics and other disciplines, including in medical imaging, and typically their eigenvalues have valuable scientific interpretations. We design pivotal bootstrap hypothesis tests of specified eigenvalues or eigenvalue multiplicities in one-sample situations and for equal eigenvalues in k-sample situations. Our tests are more broadly applicable than existing tests by allowing very general distributions, allowing three or more…

组成分布的得分匹配估计AI 解读

Compositional data are challenging to analyse due to the non-negativity and sum-to-one constraints on the sample space. With real data, it is often the case that many of the compositional components are highly right-skewed, with large numbers of zeros. Major limitations of currently available models for compositional data include one or more of the following: insufficient flexibility in terms of distributional shape; difficulty in accommodating zeros in the data in…

球面上仿射等变空间中位数的类似估计量AI 解读

Robust estimation of location for data on the unit sphere Sp−1 is an important problem in directional statistics even though the influence functions of the sample mean direction and other location estimators are bounded. A significant limitation of previous literature on this topic is that robust estimators and procedures have been developed under the assumption that the underlying population is rotationally symmetric. This assumption often does not hold with real data and…

基于标志点高斯模型的大小与形状数据回归AI 解读

In this article, we propose a regression model for size-and-shape response data. So far as we are aware, few such models have been explored in the literature to date. We assume a Gaussian model for labeled landmarks; these landmarks are used to represent the random objects under study. The regression structure, assumed in this article to be linear in the ambient space, enters through the landmark means. Two approaches to parameter estimation are considered. The first…

古地磁方向数据的缩放 von Mises–Fisher 分布与回归模型AI 解读

We propose a new distribution for analyzing paleomagnetic directional data, that is, a novel transformation of the von Mises–Fisher distribution. The new distribution has ellipse-like symmetry, as does the Kent distribution; however, unlike the Kent distribution the normalizing constant in the new density is easy to compute and estimation of the shape parameters is straightforward. To accommodate outliers, the model also incorporates an additional shape parameter, which…

利用非中心卡方分布的小波系数经验贝叶斯块收缩AI 解读

Empirical Bayes approaches to the shrinkage of empirical wavelet coefficients have generated considerable interest in recent years. Much of the work to date has focussed on shrinkage of individual wavelet coefficients in isolation. In this paper we propose an empirical Bayes approach to simultaneous shrinkage of wavelet coefficients in a block, based on the block sum of squares. Our approach exploits a useful identity satisfied by the noncentral χ2 density and provides some…

一类非高斯平稳过程与随机场的分形维数估计AI 解读

We present the asymptotic distribution theory for a class of increment-based estimators of the fractal dimension of a random field of the form g{X(t)}, where g:R→R is an unknown smooth function and X(t) is a real-valued stationary Gaussian field on Rd, d=1 or 2, whose covariance function obeys a power law at the origin. The relevant theoretical framework here is “fixed domain” (or “infill”) asymptotics. Surprisingly, the limit theory in this non-Gaussian case is somewhat…

矩阵变量超几何函数的拉普拉斯近似AI 解读

In this paper we present Laplace approximations for two functions of matrix argument: the Type I confluent hypergeometric function and the Gauss hypergeometric function. Both of these functions play an important role in distribution theory in multivariate analysis, but from a practical point of view they have proved challenging, and they have acquired a reputation for being difficult to approximate. Appealing features of the approximations we present are: (i) they are fully…

方向数据置信域的改进枢轴方法AI 解读

The importance of pivoting is well established in the context of nonparametric confidence regions. It ensures enhanced coverage accuracy. However, pivoting for directional data cannot be achieved simply by rescaling. A somewhat cumbersome pivotal method, which involves passing first into a space of higher dimension, has been developed by Fisher and Hall for samples of unit vectors. Although that method has some advantages over nonpivotal techniques, it does suffer from…

指数经验似然不具有 Bartlett 可校正性AI 解读

In a recent paper, DiCiccio, Hall and Romano established that Owen's empirical likelihood is Bartlett correctable. This is an intriguing and perhaps surprising result and is the only nonparametric context in which Bartlett correctability is known to hold. An alternative, closely related nonparametric likelihood, referred to here as exponential empirical likelihood, may be constructed using Efron's method of nonparametric tilting. The purpose of this note is to show that…

用于自助法的平衡重要性重抽样AI 解读

We show that the method of importance resampling, introduced by Vernon Johns and Anthony Davison, may be enhanced by balancing the resamples. It is demonstrated that "balanced importance resampling" improves on both "balanced uniform resampling" and "random importance resampling", from the viewpoint of statistical efficiency. Moreover, the range of applications for which efficient resampling methods may be applied is extended to include statistics which are smooth functions…