Related papers: Two-sample tests for relevant differences in persi…
Persistence diagrams are common objects in the field of Topological Data Analysis. They are topological summaries that capture both topological and geometric structure within data. Recently there has been a surge of interest in developing…
We propose a framework for analyzing and comparing distributions, allowing us to design statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over…
We propose a two-sample test for high-dimensional means that requires neither distributional nor correlational assumptions, besides some weak conditions on the moments and tail properties of the elements in the random vectors. This…
We introduce a refinement of the persistence diagram, the graded persistence diagram. It is the Mobius inversion of the graded rank function, which is obtained from the rank function using the unary numeral system. Both persistence diagrams…
We derive central limit theorems for the Wasserstein distance between the empirical distributions of Gaussian samples. The cases are distinguished whether the underlying laws are the same or different. Results are based on the (quadratic)…
We introduce a test for the conditional independence of random variables $X$ and $Y$ given a random variable $Z$, specifically by sampling from the joint distribution $(X,Y,Z)$, binning the support of the distribution of $Z$, and conducting…
A persistence diagram is a finite multiset of birth-death pairs representing the lifetimes of topological features across a filtration. Persistence diagrams do not carry intrinsic spectral or kernel structures, so applications typically use…
We propose a two-sample test for large-dimensional covariance matrices in generalized elliptical models. The test statistic is based on a U-statistic estimator of the squared Frobenius norm of the difference between the two population…
This paper is concerned with inference based on the mean function of a functional time series, which is defined as a collection of curves obtained by splitting a continuous time record, e.g. into daily or annual curves. We develop a normal…
We treat the problem of testing independence between m continuous variables when m can be larger than the available sample size n. We consider three types of test statistics that are constructed as sums or sums of squares of pairwise rank…
Motivated by the need to statistically quantify differences between modern (complex) data-sets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to…
Goodness-of-fit tests based on the empirical Wasserstein distance are proposed for simple and composite null hypotheses involving general multivariate distributions. For group families, the procedure is to be implemented after preliminary…
Motivated by a neuroscience question about synchrony detection in spike train analysis, we deal with the independence testing problem for point processes. We introduce non-parametric test statistics, which are rescaled general…
We study the detection of change-points in time series. The classical CUSUM statistic for detection of jumps in the mean is known to be sensitive to outliers. We thus propose a robust test based on the Wilcoxon two-sample test statistic.…
Modern longitudinal studies collect multiple outcomes as the primary endpoints to understand the complex dynamics of the diseases. Oftentimes, especially in clinical trials, the joint variations among the multidimensional responses play a…
Asymptotic methods for hypothesis testing in high-dimensional data usually require the dimension of the observations to increase to infinity, often with an additional relationship between the dimension (say, $p$) and the sample size (say,…
We construct a two-sample test for comparison of long memory parameters based on ratios of two rescaled variance (V/S) statistics studied in [Giraitis L., Leipus, R., Philippe, A., 2006. A test for stationarity versus trends and unit roots…
Many time series exhibit changes both in level and in variability. Generally, it is more important to detect a change in the level, and changing or smoothly evolving variability can confound existing tests. This paper develops a framework…
Two-sample tests utilizing a similarity graph on observations are useful for high-dimensional and non-Euclidean data due to their flexibility and good performance under a wide range of alternatives. Existing works mainly focused on sparse…
Persistence diagrams are objects that play a central role in topological data analysis. In the present article, we investigate the local and global geometric properties of spaces of persistence diagrams. In order to do this, we construct a…