Related papers: Two Sample Test for Extrinsic Antimeans on Planar …

Methods of hypotheses testing for equality of extrinsic antimeans on compact manifolds are unveiled in this paper. The two and multiple sample problem for antimeans on compact manifolds is addressed for large samples via asymptotic…

In this paper after a brief revision of VW-means, which are extrinsic means on real and complex projective spaces, relative to the Veronese-Whitney embeddings, we give two examples of sample VW means computations on planar Kendall shape…

This article develops nonparametric inference procedures for estimation and testing problems for means on manifolds. A central limit theorem for Frechet sample means is derived leading to an asymptotic distribution theory of intrinsic…

Various concepts of mean shape previously unrelated in the literature are brought into relation. In particular for non-manifolds such as Kendall's 3D shape space, this paper answers the question, for which means one may apply a two-sample…

Confidence sets from i.i.d. data are constructed for the extrinsic mean of a probabilty measure P on spheres, real projective spaces, and complex projective spaces, as well as Grassmann manifolds, with the latter three embedded by the…

Kernel methods have had great success in Statistics and Machine Learning. Despite their growing popularity, however, less effort has been drawn towards developing kernel based classification methods on Riemannian manifolds due to difficulty…

Motivated by the problem of nonparametric inference in high level digital image analysis, we introduce a general extrinsic approach for data analysis on Hilbert manifolds with a focus on means of probability distributions on such sample…

We propose a new definition of the chi-square divergence between distributions. Based on convexity properties and duality, this version of the {\chi}^2 is well suited both for the classical applications of the {\chi}^2 for the analysis of…

We introduce a new test procedure of independence in the framework of parametric copulas with unknown marginals. The method is based essentially on the dual representation of $\chi^2$-divergence on signed finite measures. The asymptotic…

This paper introduces an approach for detecting differences in the first-order structures of spatial point patterns. The proposed approach leverages the kernel mean embedding in a novel way by introducing its approximate version tailored to…

Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical…

In this paper we consider testing the equality of probability vectors of two independent multinomial distributions in high dimension. The classical chi-square test may have some drawbacks in this case since many of cell counts may be zero…

Discrete forms of the mean and directed curvature are constructed on piecewise flat manifolds, providing local curvature approximations for smooth manifolds embedded in both Euclidean and non-Euclidean spaces. The resulting expressions take…

We study smooth, proper embeddings of noncompact surfaces in 4-manifolds, focusing on exotic planes and annuli, i.e., embeddings pairwise homeomorphic to the standard embeddings of R^2 and R^2-int D^2 in R^4. We encounter two uncountable…

Testing the equality of the covariance matrices of two high-dimensional samples is a fundamental inference problem in statistics. Several tests have been proposed but they are either too liberal or too conservative when the required…

This paper explores methods for estimating or approximating the total variation distance and the chi-squared divergence of probability measures within topological sample spaces, using independent and identically distributed samples. Our…

We propose a nonparametric two-sample test procedure based on Maximum Mean Discrepancy (MMD) for testing the hypothesis that two samples of functions have the same underlying distribution, using kernels defined on function spaces. This…

In this study, we develop nonparametric analysis of deviance tools for generalized partially linear models based on local polynomial fitting. Assuming a canonical link, we propose expressions for both local and global analysis of deviance,…

We consider goodness-of-fit tests for uniformity of a multinomial distribution by means of tests based on a class of symmetric statistics, defined as the sum of some function of cell-frequencies. We are dealing with an asymptotic regime,…

In this paper we apply techniques from nonstandard analysis to study expansive dynamical systems. Among other results, we provide a necessary and sufficient condition for an expansive homeomorphism on a compact metric space to admit…