Empirical likelihood for manifolds
针对取值于非欧度量空间的流形数据，发展了非参数似然概念，并基于经验似然理论提出推断弗莱歇均值及相关总体对象的方法，包括两样本检验、方差推断等，模拟和实例显示其优于传统沃尔德检验。
Abstract There has been growing interest in statistical analysis of random objects taking values in a non-Euclidean metric space. One important class of such objects consists of data on manifolds. This article is concerned with inference on the Fréchet mean and related population objects on manifolds. We develop the concept of nonparametric likelihood for data on manifolds and propose general inference methods by adapting the theory of empirical likelihood. In addition to the basic asymptotic properties, such as Wilks’ theorem of the empirical likelihood statistic, we present several generalizations of the proposed methodology: two-sample testing, inference on the Fréchet variance, quasi-Bayesian inference, local Fréchet regression, and estimation of the Fréchet mean set. Simulation and real data examples illustrate the usefulness of the proposed methodology and its advantage against the conventional Wald test.